Articoli accademici

We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT (GPT-5.5 Thinking) and Google Gemini Advanced (Gemini 1.5 Pro), we show that Bell's inequalities are significantl…

[Traduzione in italiano] Debates about whether large language models (LLMs) genuinely understand the language they produce often rest on the assumption that understanding necessarily entails conscious experience. In this article, we argue that this assumption is unwarranted. By drawing a principl…

The phenomenon of quantum tunneling challenges classical intuitions about particle behavior and offers profound insights into the nature of quantum entities. This article examines tunneling through the lens of an effect predicted by Thomas E. Hartman in 1962: the tunneling time-delay becomes inde…

Quantum mechanics has maintained over the years the reputation of being “the most obscure theory.” It works perfectly well, but nobody seems to know why. It has been argued that the difficulty in understanding quantum theory is our failed attempt to force onto it a wrong conceptual scheme, wantin…

An overview of the conceptuality interpretation of quantum mechanics is presented, along with an explanation of how it sheds light on key quantum and relativistic phenomena. In particular, we show how the interpretation clarifies Heisenberg's uncertainty principle, wave function-based and entangl…

The conceptuality interpretation of quantum mechanics proposes that quantum entities have a conceptual nature, interacting with the material world through processes that are the physical counterpart of the meaning-based processes, which typically occur in human cognition. This interpretation emer…

Quantum cognition has made it possible to model human cognitive processes very effectively, revealing numerous parallels between the properties of conceptual entities tested by the human mind and those of microscopic entities tested by measurement apparatuses. The success of quantum cognition has…

Einstein’s article on the Einstein-Podolsky-Rosen paradox is the most cited of his works, but not many know that it was not fully representative of the way he thought about the incompleteness of the quantum formalism. Indeed, his main worry was not Heisenberg’s uncertainty principle, which he acc…

Identical systems, or ‘entities’, are ‘indistinguishable’ in quantum mechanics (QM), and the ‘symmetrization postulate’ rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis of the historical development of QM attributes the ori…

L’approccio alla coscienza di Federico Faggin e Giacomo Mauro D’Ariano, denominato quantum information-based panpsychism (QIP), sostiene che coscienza e libero arbitrio sono proprietà intrinseche degli stati quantistici puri. Metto tale prospettiva a confronto con l’interpretazione concettualisti…

We present a theoretical and empirical investigation of the statistical behaviour of the words in a text produced by human language. To this aim, we analyse the word distribution of various texts of Italian language selected from a specific literary corpus. We firstly generalise a theoretical fra…

An operational approach to quantum mechanics has been developed in the past decades in our group in Brussels. A similar approach is taken in this work, making use of the extra operational depth offered by this approach, to show that the construction of spacetime is specific to each observer. What…

We consider a simple string model to explain and partly demystify the phenomenon of quantum entanglement. The model in question has nothing to do with string theory: it uses macroscopic strings that can be acted upon by Alice and Bob in ways that violate, or fail to violate, in different ways Bel…

In their recent articles Gruber, Block and Montemayor (2022: Front. Psychol., 13, 718505) and Buonomano and Rovelli (2022: arXiv:2110.01976) discuss the differences between time in physics and psychology. With the aim of commenting on their views, we first outline a few general aspects of relativ…

Yoichi Kaya era un economista giapponese, studioso di politiche energetiche. In questo articolo vi parlo della sua famosa equazione, o identità, che scrisse circa una trentina d’anni fa. L’equazione è molto semplice da derivare, cosa che faremo assieme. Non permette, ovviamente, di risolvere i pr…

In forma di conversazione-intervista, l’articolo presenta la figura di Giovanni Sassoli de Bianchi e la genesi del progetto dei Villaggi Sovrani: piccoli habitat autonomi, etici e solidali, pensati come risposta concreta alla crescente conflittualità, all’inerzia degli Stati moderni, agli sprechi…

The view exists that Bell-tests would only be about local incompatibility of quantum observables and that quantum non-locality would be an unnecessary concept in physics. In this note, we emphasize that it is not incompatibility at the local level that is important for the violation of Bell-CHSH …

It is well known that correlations produced by common causes in the past cannot violate Bell’s inequalities. This was emphasized by Bell in his celebrated example of Bertlmann’s socks. However, if common causes are induced by the very measurement process i.e., actualized at each run of a joint me…

Seguendo le orme di Schrödinger, proponiamo una visione unificata della materia, della vita e della cultura umana, con particolare attenzione al ruolo svolto dalla seconda legge della termodinamica e dalla separazione primordiale tra materia e antimateria. Così facendo, mettiamo in evidenza la fr…

Following in the footsteps of Schrödinger, we propose a unified view of matter, life and human culture, with particular emphasis on the role played by the second law of thermodynamics and the primordial matter-antimatter separation. In doing so, we highlight the fragility of ‘construction’ (order…

This special issue is one of the outcomes of the International Symposium “Worlds of Entanglement,” held at the Free University of Brussels (VUB), on September 29–30, 2017. The event gathered more than 50 scholars from different disciplines, ranging from pure mathematics to visual arts, and from m…

We describe a simple experimental setting where joint measurements performed on a single (classical or quantum) entity can violate both the Bell-CHSH inequality and the marginal laws (also called no-signaling conditions). Once emitted by a source, the entity propagates within the space of Alice’s…

Questo articolo si basa su un mio intervento al corso “Cibo e pensiero”, organizzato dall’Ospedale San Raffaele e svoltosi il 24 e 27 settembre 2021. Durante questo corso online, si sono avvicendati scienziati con diverse competenze, ma anche filosofi e giornalisti, in un confronto interdisciplin…

Questo articolo è una versione ampliata di una breve conferenza-intervista che ho avuto il piacere di dare via Web, il 1° giugno 2020, nell’ambito di un ciclo di otto incontri intitolati “pillole per la mente”, il cui scopo era parlare di come l’alimentazione influenzi le nostre capacità cognitiv…

In questo articolo, offro alcuni spunti circa la possibilità di sperimentare i benefici, sia fisici che mentali, di una pratica di contatto con il freddo intenso. Nella prima parte, racconterò di come mi sono avvicinato a questa possibilità, riproponendo alcuni post che scrissi nel 2019, su Faceb…

Chiarisco un comune malinteso circa i meccanismi fisiologici alla base delle tecniche respiratorie di iperventilazione. È infatti spesso convinzione errata di molti praticanti che aumentando il ritmo respiratorio si ottenga un’iperossigenazione dell’organismo, quando invece accade esattamente l’o…

It is generally assumed, and usually taken for granted, that reality is fully contained in space. However, when taking a closer look at the strange behavior of the entities of the micro-world, we are forced to abandon such a prejudice and recognize that space is just a temporary crystallization o…

In a very educational article, François Ost took us through different readings of the ancient Bedouin parable of the camels. In this note, we observe that the judge’s stratagem of introducing ath camel, which is ultimately returned to him, not only allows for solving the dispute, in pragmatic ter…

According to the view of multiplex realism, which will be presented and motivated in this article, our three-dimensional Euclidean theater is only one among many theaters that can be conceived and constructed, to stage the whole of our reality. The view of a ‘multiplex reality’ has consequences n…

How can we explain the strange behavior of quantum and relativistic entities? Why do they behave in ways that defy our intuition about how physical entities should behave, considering our ordinary experience of the world around us? In this article, we address these questions by showing that the c…

The objectives of the Center Leo Apostel for Interdisciplinary Studies were summarized by his creator as: interdisciplinarity, construction of world views and broad dissemination of scientific knowledge. In compliance with the third of these objectives, we provide a rigorous but accessible popula…

This special issue is one of the outcomes of the International Symposium “Worlds of Entanglement,” held at the Free University of Brussels (VUB), on September 29–30, 2017. The event gathered more than 50 scholars from different disciplines, ranging from pure mathematics to visual arts, and from m…

We model a typical Bell-test experimental situation by considering that Alice and Bob perform incompatible measurements in a sequential way, with mixed orders of execution. After emphasizing that order effects will generally produce a violation of the marginal laws, we derive an upper limit for t…

We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence measurements are considered, the violation of the ‘marginal la…

We show that the Brussels operational-realistic approach to quantum physics and quantum cognition offers a fundamental strategy for modeling the meaning associated with collections of documental entities. To do so, we take the World Wide Web as a paradigmatic example and emphasize the importance …

Physical entities are not truly teleported in so-called quantum teleportation, only their states are. Similarly, physical entities are not truly cloned in so-called quantum cloning, only their states are. The celebrated no-cloning theorem tells us that a universal cloning machine, able to perfect…

Since its inception, many physicists have seen in quantum mechanics the possibility, if not the necessity, of bringing cognitive aspects into the play, which were instead absent, or unnoticed, in the previous classical theories. In this article, we outline the path that led us to support the hypo…

The probability of quantum relocation of a human body, at a given distance, is estimated using two different methods, giving comparable results. Not only the obtained values for the probabilities are inconceivably small, but assumptions of a sci-fi nature are also necessary to ensure that they ar…

This is an article written in a popular science style, in which I will explain: (1) the famous Heisenberg uncertainty principle, expressing the experimental incompatibility of certain properties of micro- physical entities; (2) the Compton effect, describing the interaction of an electromagnetic …

We show that the extended Bloch representation of quantum mechanics also applies to infinite-dimensional entities, to the extent that the number of (possibly infinitely degenerate) outcomes of a measurement remains finite, which is always the case in practical situations.Aerts, D. & Sassoli de Bi…

In psychological measurements, two levels should be distinguished: the individual level, relative to the different participants in a given cognitive situation, and the collective level, relative to the overall statistics of their outcomes, which we propose to associate with a notion of collective…

We motivate the possibility of using notions and methods derived from quantum physics, and more specifically from the research field known as ‘quantum cognition’, to optimally model different situations in the field of medicine, its decision-making processes and ensuing practices, particularly in…

The Einstein-Podolsky-Rosen (EPR) paradox was enunciated in 1935 and since then it has made a lot of ink flow. Being a subtle result, it has also been largely misunderstood. Indeed, if questioned about its solution, many physicists will still affirm today that the paradox has been solved by the B…

The text presents a dialogue between several scholars discussing the nature of reality and the role of observation in shaping our understanding of it. The conversation explores the concepts of balance and unbalance, with Diederik arguing that reality is characterized by a constant struggle for st…

We present a view of the evolving reality based on our understanding of the recently discovered (in the time scale of human evolution) quantum laws, how they manifest at the different organizational levels of inert matter, living organisms and cultural artifacts, and what they possibly imply rega…

In the first half of this two-part article (Aerts et al. in Found Sci. doi:10.1007/s10699-017-9528-9, 2017b), we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and…

We present a cognitive psychology experiment where participants were asked to select pairs of spatial directions that they considered to be the best example of Two different wind directions. Data are shown to violate the CHSH version of Bell’s inequality with the same magnitude as in typical Bell…

We present the fundamentals of the quantum theoretical approach we have developed in the last decade to model cognitive phenomena that resisted modeling by means of classical logical and probabilistic structures, like Boolean, Kolmogorovian and, more generally, set theoretical structures. We firs…

We elaborate a quantum model for the meaning associated with corpora of written documents, like the pages forming the World Wide Web. To that end, we are guided by how physicists constructed quantum theory for microscopic entities, which unlike classical objects cannot be fully represented in our…

The term observer effect generally refers to the possibility that an act of observation may affect the properties of what is observed. However, depending on the context and the mechanisms involved, it may indicate effects of a very different nature. Observer effects are a threat to validity in mu…

In recent years, the mathematical structure of quantum theory has been successfully employed in different areas beyond physics, such as biology, economics, psychology and computer science. This special issue aims precisely at setting a landmark with respect to the benefits in applying and cross-f…

The mathematical formalism of quantum theory exhibits significant effectiveness when applied to cognitive phenomena that have resisted traditional (set theoretical) modeling. Relying on a decade of research on the operational foundations of micro-physical and conceptual entities, we present a the…

The ‘quantum cognition’ paradigm was recently challenged by its proven impossibility to simultaneously model ‘question order effects’ and ‘response replicability’. In the present article we describe sequential dichotomic measurements within an operational and realistic framework for human cogniti…

A general tension-reduction (GTR) model was recently considered (Aerts and Sassoli de Bianchi 2015a, 2015b) to derive quantum probabilities as (universal) averages over all possible forms of non-uniform fluctuations and explain their considerable success in describing experimental situations also…

In 1975, two experimental groups have independently observed the 4π-symmetry of neutrons’ spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach Zehnder interferometer of light optics). In this article, w…

The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner’s possibilist transactional interpretation (PTI) of quantum mechanics — an extension of Cramer’s transactional interpretation — and the authors’ hidden-measurement interpretation (…

The ‘conjunction fallacy’ has been extensively debated by scholars in cognitive science and, in recent times, the discussion has been enriched by the proposal of modeling the fallacy using the quantum formalism. Two major quantum approaches have been put forward: the first assumes that respondent…

The quantum formalism can be completed by assuming that density operators also represent genuine states. An ‘extended Bloch representation’ (EBR) then results, in which not only the states but also the measurement-interactions can be described. Consequently, the Born rule can be obtained as an ex…

The standard Bloch sphere representation has been recently generalized to describe not only systems of arbitrary dimension, but also their measurements, in what has been called the extended Bloch representation of quantum mechanics. This model, which offers a solution to the longstanding measurem…

The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we expose the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These fo…

We present a very general geometrico-dynamical description of physical or more abstract entities, called the general tension-reduction (GTR) model, where not only states, but also measurement-interactions can be represented, and the associated outcome probabilities calculated. Underlying the mode…

An extended Bloch representation of quantum mechanics was recently derived to offer a possible (hidden-measurements) solution to the measurement problem. In this article we use this representation to investigate the geometry of superposition and entangled states, explaining interference effects a…

Entangled states are in conflict with a general physical principle which expresses that a composite entity exists if and only if its components also exist, and the hypothesis that pure states represent the actuality of a physical entity, i.e., its ‘existence’. A possible way to solve this paradox…

Many advocates of the Everettian interpretation consider that theirs is the only approach to take quantum mechanics really seriously, and that this approach allows to deduce a fantastic scenario for our reality, one that consists of an infinite number of parallel worlds that branch out continuous…

In the first part of this two-part article (Aerts & Sassoli de Bianchi, 2014), we have introduced and analyzed a multidimensional model, called the general tension-reduction (GTR) model, able to describe general quantum-like measurements with an arbitrary number of outcomes, and we have used it a…

We introduce a model which allows to represent the probabilities associated with an arbitrary measurement situation as it appears in different domains of science–from cognitive science to physics–and use it to explain the emergence of quantum probabilities (the Born rule) as uniform fluctuations …

We investigate indeterminism in physical observations. For this, we introduce a distinction between genuinely indeterministic (creation-1 and discovery-1) observational processes, and fully deterministic (creation-2 and discovery-2) observational processes, which we analyze by drawing a parallel …

We present some of the foundational ideas of so-called hidden-measurement interpretation of quantum mechanics, whose proposed solution to the measurement problem does not require any deus ex machina intervention from an abstract ego, but asks in exchange to accept that our physical reality would …

So far, astrology has not been able to produce significant statistical correlations. However, certain individuals could use it with some benefit in their self-research and self-development. In this article, I propose a tentative speculative solution to this paradox, based on the consciential (mul…

A generalized Bloch sphere, in which the states of a quantum entity of arbitrary dimension are geometrically represented, is investigated and further extended, to also incorporate the measurements. This extended representation constitutes a general solution to the measurement problem, inasmuch it…

Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox contains two different problems: an “easy” problem and a “hard” problem. The easy problem can be solve…

Diederik Aerts was the first in the eighties to develop a concrete example of a macroscopic “classical” entity violating Bell’s inequalities (BI). In more recent years, he also developed a macroscopic model in which the amount of non-locality and indeterminism can be continuously varied, and used…

In a letter to Born, Einstein wrote: "Quantum mechanics is certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says a lot, but does not really bring us any closer to the secret of the old one. I, at any rate, am convinced that He does not throw dice." In …

We comment on a recent paper by Hobson, explaining that quantum "fields" are no more fields than quantum "particles" are particles, so that the replacement of a particle ontology by an all-field ontology cannot solve the typical interpretational problems of quantum mechanics.Sassoli de Bianchi, M…

Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the observation is a purely non-invasive discovery process; …

My personal perspective regarding the question addressed by Jean Burns is that there is a serious conceptual difficulty in the way most physicists and parapsychologists are approaching today both quantum entanglement and extrasensory perception (ESP). By this I don’t mean to say that ESP and quan…

From the beginning of his research, the Belgian physicist Diederik Aerts has shown great creativity in inventing a number of concrete machine-models that have played an important role in the development of general mathematical and conceptual formalisms for the description of the physical reality.…

La proiezione della coscienza è un fenomeno naturale, conseguenza dell’anatomia e fisiologia del nostro olosoma. Scopo principale dello studio di questo fenomeno, e delle tecniche in grado di favorirlo, è poterne assumere il controllo, trasformando quella che solitamente è un’esperienza vissuta i…

The concept of energy is central in all of modern science, and is obviously of great importance also in the study of the psychoenergetic phenomena. However, both among conventional physicists and less conventional researchers of parapsychic phenomena, there still is some confusion about a proper …

The validity of the assertion that some recent double-slit interference experiments, conducted by Radin et al. [Phys. Essays 25, 157 (2012)], would have tested the possible role of the experimenter’s mind in the collapse of the quantum wave function is questioned. It is emphasized that quantum me…

The purpose of this article is threefold. Firstly, it aims to present, in an educational and non-technical fashion, the main ideas at the basis of Aerts’ creation-discovery view and hidden measurement approach: a fundamental explanatory framework whose importance, in this author’s view, has been …

The main scope of this essay is to inform the new generations of students, teachers and researchers about the possibility of adopting a new integral approach in science, which is the one of self-research. By doing so, I will also explain why self-research is still not promoted on a large scale on…

We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the m…

We consider the classical concept of time of permanence and observe that its quantum equivalent is described by a bona fide self-adjoint operator. Its interpretation, by means of the spectral theorem, reveals that we have to abandon not only the idea that quantum entities would be characterizable…

La capacità di osservare la realtà per quello che è, e non per quello che pensiamo debba essere, è essenziale per la nostra progressione interiore. Purtroppo, il processo di osservazione si arresta molto presto nella nostra vita, così come l’apprendimento, la crescita e l’evoluzione. Viviamo quin…

Using everyday macroscopic entities as guiding examples, we clarify the content of two important results of the beginning of twentieth century: Einstein-Podolsky-Rosen's reality criterion and Heisenberg's uncertainty principle. We then use them in combination to conclude that our widespread belie…

In this note we use the notion of time-delay to explain the physical content of the transformation properties of transmission and reflection amplitudes, as a result of a displacement of the potential. Then, we reconsider the recent analysis of the scattering problem by a finite-periodic potential…

In a recent paper, Giust et al. showed how the elements of the 2x2 scattering matrix of a one-dimensional system composed of two subsystems can be expressed in terms of the scattering amplitudes of the individual subsystems to generalize Einstein’s composition law of velocities. We note that this…

After having emphasized some fundamental analogies between Yoga and Conscientiology, we propose to combine the practice of a specific pranayama, called Circular Breathing (CB), with the technique of the Voluntary Energetic Longitudinal Oscillation (VELO), to promote a procedure as gradual and eff…

I was more than pleased to read Dave’s appreciative review-letter of my two-part Dialogue about Science, Reality and the Consciousness. His interesting comments, for which I thank him, give me the opportunity to further clarify some of the fundamental topics that were addressed in the essay.Sasso…

A simple mass model is presented to explain the energetic separation between the physical and extraphysical dimensions. The model is also used to understand the function of the holochakra as a mediator structure which can considerably increase the efficiency of interdimensional energy transfer.Sa…

In a recent paper, Bashkansky and Netzer considered a one-dimensional elastic collision between a target particle of mass m and an incident particle of mass M [...]⁠. Sassoli de Bianchi, M. (2007). Comment on “The role of mediation in collisions and related analogs,” by E. Bashkansky and N. Netze…

This paper is the continuation and conclusion of a Socratic dialogue between a lecturer and a student, whose first part appeared in (Sassoli de Bianchi, 2007). In a non-technical style, the dialogue presents some elements for a general and operational description of reality. In this second part, …

This paper is written as a Socratic dialogue between a lecturer and a student. In a non-technical style, it presents some elements for an operational description of reality. Following a brief introductory discussion about the main characterizing ingredients of a scientific approach to reality, th…

This article is a conceptual speculative statement about the origin and structure of our reality. We propose to view the consciousnesses’ holosomas as living holotheories of reality, evolving through the instrument of theorice and producing a fractal structuring of reality as a whole. We hypothes…

In a recent article, Michael Ross invite us to consider the following question (Ross, Michael, 2005): “Why are OBE’s (and psychic/spiritual events and talents in all their manifestations) so difficult to empirically prove under scientifically valid conditions?”. In his article, the author present…

We present a very simple semiclassical derivation of Hartman’s effect valid for potential barriers of general shape. The derivation also gives some insight into the tunnelling time phenomenon.Sassoli de Bianchi, M. (2000). A Simple semiclassical derivation of Hartman’s effect. Eur. J. Phys. 21, p…

We show that, contrary to what would be expected on the basis of the mass barrier model, the transmission probability for the one-dimensional scattering problem with position-dependent mass normally tends to unity as energy goes to infinity, provided the mass is a continuous function of position.…

A comprehensive introduction to the basic formalism of the one-dimensional scattering by time-periodic short-ranged potentials is presented. The fundamental objects of the theory (transmission and reflexion probabilities, sidebands and time delays) are defined, and a generalized Born expansion de…

In their recent paper, Aktosun, Klaus, and van der Mee considered the problem of factorization of the scattering matrix for the one-dimensional Schrödinger equation and two of its generalizations (wave propagation in a nonhomogeneous medium and wave propagation in a nonconservative medium), and t…

Using simple time-dependent methods, we study the phenomenon of dynamical capture in non-relativistic quantum mechanics. We show that for time-dependent potentials that are asymptotically constant in time, the probability of an incoming particle becoming trapped in the interaction region is in ge…

We give a simple and general description of the bound-state structure of a one-dimensional finite superlattice as a function of its perioddand some quantities characterizing the single unit cell.Sassoli de Bianchi, M. and Di Ventra, M. (1996). How many bound-states does a one-dimensional finite s…

A recent result by Fu [Phys. Lett. A 205 (1996) 419] can be found in textbooks. His assertion of the unobservability of an additional arbitrary phase factor is disputed.Sassoli de Bianchi, M. (1996). Comment on “Relative phase between quantum transmission and reflection amplitudes in one dimensio…

Levinson’s theorem is generalized to quantum scattering with time-periodic potentials. The zero-energy limit of the phase shift in the elastic channel is linked to the number of bound (cyclic) states of the time-dependent potential by the same relation as in the static case.Martin, Ph. A. and Sas…

Dans cette thèse on aborde divers aspects de la diffusion par potentiel en mécanique quantique non-relativiste. Dans la première partie, nous étudions le concept de temps de retard. Plus précisément, après une introduction élémentaire à la théorie (chapitre I), nous clarifions au chapitre II le r…

The variable phase method is applied to the one-dimensional Schrödinger equation with position-dependent (effective) mass, to derive first-order differential equations for the transmission and reflection amplitudes, and bound-state energies, which are particularly convenient for numerical computa…

Using time-dependent methods, we study the scattering of a quantum mechanical particle by short-range potentials with very slow or very fast periodic variations in time. The low- and high-frequency limits are derived as well as their fist non-vanishing corrections, and their physical significance…

Bound states and zero‐energy resonances of one‐dimensional finite periodic potentials are investigated, by means of Levinson’s theorem. For finite range potentials supporting no bound states, a lower bound for the (reduced) time delay at threshold is derived.Sassoli de Bianchi, M. and Di Ventra, …

The passage of a spin-1/2 neutral particle through a region of uniform magnetic field and the corresponding precession mechanism is analyzed from the viewpoint of scattering theory, with particular consideration of the role of the field boundaries.Martin, Ph. A. & Sassoli de Bianchi, M. (1994). S…

The one-dimensional Levinson’s theorem is derived and used to study zero-energy resonances in a double-potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy …

We give a general and mathematically precise definition of the notion of conditional time delay in scattering theory i.e., a notion of time delay for a given condition of observation of the scattered particle. A formula, generalising the Eisenbud-Wigner time delay formula, is derived. The basic c…

We show that the time delay of a scattering process, defined as the difference of interacting and free sojourn times for increasing spatial regions, can only exist for sequences of dilated balls. The transformation properties of the Eisenbud-Wigner formula under translations are discussed.Martin,…

Using the time-dependent scattering theory the authors prove that, in any spatial dimension and for arbitrary spin, the reading of the Larmor clock agrees with the global Eisenbud-Wigner time delay in the limit of an infinitesimal magnetic field. They show that convergence is also achieved at fix…

Ce travail a pour objet l’analyse de la notion de degré de dépendance aléatoire. Il s’agit d’une notion de caractère mathématique dont le cadre est celui de la théorie des probabilités. C’est pourquoi nous avons choisi de commencer ce mémoire par une courte introduction aux concepts fondamentaux …