Top Research Papers on Quantum Mechanics

Quantum statistical mechanics governs metals, semiconductors, and neutron stars. Statistical mechanics spawned Planck’s invention of the quantum, and explains Bose condensation, superfluids, and superconductors. This chapter briefly describes these systems using mixed states, or more formally density matrices, and introducing the properties of bosons and fermions. We discuss in unusual detail how useful descriptions of metals and superfluids can be derived by ignoring the seemingly important interactions between their constituent electrons and atoms. Exercises explore how gregarious bosons lea...

We showed in a recent article (Lawrence et. al., 2023, Quantum 7, 1015), that relative facts (outcomes), a central concept in Relational Quantum Mechanics, are inconsistent with Quantum Mechanics. We proved this by constructing a Wigner-Friend type sequential measurement scenario on a Greenberger-Horne-Zeilinger (GHZ) state of three qubits, and making the following assumption:"if an interpretation of quantum theory introduces some conceptualization of outcomes of a measurement, then probabilities of these outcomes must follow the quantum predictions as given by the Born rule."Our work has been...

Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory \cite{Rovelli.21}. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system S and an observer A without decoherence, and (ii) such an outcome is a "fact" relative to the observer A, but it is not a fact relative to another observer B who has not interacted with S or A during the foregoing measurement process. For B the system S⊗A remains entangled. We derive a GHZ-like contradiction showing that relative facts described by the...

This popular undergraduate quantum mechanics textbook is now available in a more affordable printing from Cambridge University Press. Unlike many other books on quantum mechanics, this text begins by examining experimental quantum phenomena such as the Stern-Gerlach experiment and spin measurements, using them as the basis for developing the theoretical principles of quantum mechanics. Dirac notation is developed from the outset, offering an intuitive and powerful mathematical toolset for calculation, and familiarizing students with this important notational system. This non-traditional approa...

Carbocations play key roles in classical organic reactions and have also been implicated in several enzyme families. A hallmark of carbocation chemistry is multitudes of competing reaction pathways, and to be able to distinguish between pathways with quantum chemical calculations, it is necessary to approach chemical accuracy for relative energies between carbocations. Here, we present an extensive study of the performance of selected density functional theory (DFT) methods in describing the thermochemistry and kinetics of carbocations and their corresponding neutral alkenes both in the gas-ph...

This original and innovative textbook takes the unique perspective of introducing and solving problems in quantum mechanics using linear algebra methods, to equip readers with a deeper and more practical understanding of this fundamental pillar of contemporary physics. Extensive motivation for the properties of quantum mechanics, Hilbert space, and the Schrödinger equation is provided through analysis of the derivative, while standard topics like the harmonic oscillator, rotations, and the hydrogen atom are covered from within the context of operator methods. Advanced topics forming the basi...

Quantum mechanics presently has many unanswered questions, paradoxes, and even outright logical contradictions. To make progress in understanding quantum mechanics, we begin by proposing that relativity be set aside in favor of an absolute aetherial theory. Once that step is taken, we can understand quantum collapse as a description of real wave-packets collapsing in a faster-than-light way. By assuming that a partially observable reality exists, we can then extend our analysis of wave-packets into the subquantum, and the Heisenberg uncertainty principle then follows from the Fourier uncerta...

Among the famous formulations of quantum mechanics, the stochastic picture developed since the middle of the last century remains one of the less known ones. It is possible to describe quantum mechanical systems with kinetic equations of motion in configuration space based on conservative diffusion processes. This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. The mathematical foundations of this approach were laid by Edward Nelson in 1966. It allows a different perspective on quantum phenomena without necessarily using the w...

Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptio...

We introduce a geometric path integral definition of wormhole partition functions in a general class of 1D quantum systems obtained by quantizing a phase space. We compute the wormhole partition function in a semi-classical limit and in some simple examples. The partition function of the n-fold wormhole is found to be identical to the n-th Renyi entropy of a thermal mixed state of the doubled system. This mixed state incorporates three types of quantum statistical behavior: classically correlated, quantum entangled, and classically uncorrelated. We apply our prescription to 2D CFTs with Viraso...

Regarded as one of the most fundamental concepts of classical mechanics and thermodynamics, work has received well-grounded definitions within the quantum framework since the 1970s, having being successfully applied to many contexts. Recent developments on the concept have taken place in the emergent field of quantum thermodynamics, where work is frequently characterized as a stochastic variable. Notwithstanding this remarkable progress, it is still debatable whether some sensible notion of work can be posed for a strictly quantum instance involving a few-particle system prepared in a pure sta...

We propose a reformulation of quantum mechanics in which the distinction between definite and indefinite becomes the fundamental primitive. Inspired by suggestions of Heisenberg, Schrodinger and Dyson that the past can't be described in terms of wavefunctions and operators, so that the uncertainty principle does not apply to past events, we propose that the distinction between past, present and future is derivative of the fundamental distinction between indefinite and definite. %The same is the case for the quantum world versus classical world distinction of the Copenhagen interpretation. We t...

The ground state of SCMS theory obtained using the VQE computation with the exact solution is compared and the implications of the the numerical simulation of SCQM on a quantum computer for the simulation of quantum gravity in light of the Anti-de Sitter/Superconformal field theory (AdS/CFT).

In this work, the operator-sum representation of a quantum process is extended to the probability representation of quantum mechanics. It is shown that each process admitting the operator-sum representation is assigned a kernel, convolving of which with the initial tomogram set characterizing the system state gives the tomographic state of the transformed system. This kernel, in turn, is broken into the kernels of partial operations, each of them incorporating the symbol of the evolution operator related to the joint evolution of the system and an ancillary environment. Such a kernel decomposi...

A model based on finite quantum mechanics for a constructive study of decompositions of quantum systems based on Hilbert spaces with composite dimension is proposed.

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows...

A proposal of how to complete non-relativistic quantum mechanics to a physically meaningful, mathematically precise and logically coherent theory is reviewed. Our proposal leads to a general, non-linear stochastic law for the time-evolution of states of individual physical systems. An application of the general formalism to the quantum theory of fluorescence of an atom coupled to the radiation field is sketched. Some remarks on relativistic quantum theory conclude our review.

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is given by elements of the permutation group. This would restore an ontological interpretation. It is shown how, at low energies per particle degree of freedom, almost any quantum system allows for such a transformation. This contradicts Bell’s theorem, and we emphasise why some of the assumptions made by Bell to prove his theorem cannot hold for the models stud...

It has been claimed that no protocol for measuring quantum work can satisfy standard physical principles, casting doubts on the compatibility between quantum mechanics, thermodynamics, and the classical limit. In this Letter, we present a solution for this incompatibility. We demonstrate that the standard formulation of these principles fails to address the classical limit properly. By proposing changes in this direction, we prove that all the essential principles can be satisfied when work is defined as a quantum observable, reconciling quantum work statistics and thermodynamics. Pub...

The traditional view from particle physics is that quantum gravity effects should only become detectable at extremely high energies and small length scales. Due to the significant technological challenges involved, there has been limited progress in identifying experimentally detectable effects that can be accessed in the foreseeable future. However, in recent decades, the size and mass of quantum systems that can be controlled in the laboratory have reached unprecedented scales, enabled by advances in ground-state cooling and quantum-control techniques. Preparations of massive systems in quan...

The results suggest that the combination of protein evolutionary and ELF analyses provides insights into residue/molecular fragment selection for QM/MM simulations.

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In this paper the problem of tomographic reconstruction of states is investigated within the so-called Schwinger’s picture of quantum mechanics in which a groupoid is associated with every quantum system. The attention is focussed on spin tomography: in this context the groupoid of interest is the groupoid of pairs over a finite set. In a nutshell, this groupoid is made up of transitions between all possible pairs of outcomes belonging to a finite set. In addition, these transitions possess a partial composition rule, generalizing the notion of groups. The main goal of the paper consists in pr...

A quantum spin-$\frac{1}{2}$ chain with an axial symmetry is normally described by quasiparticles associated with the spins oriented along the axis of rotation. Kinetic constraints can enrich such a description by setting apart different species of quasiparticles, which can get stuck at high enough density, realising the quantum analogue of jamming. We identify a family of interactions satisfying simple kinetic constraints and consider generic translationally invariant models built up from them. We study dynamics following a local unjamming perturbation in a jammed state. We show that they can...

Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap....

We exhibit a mechanism which dynamically adjusts cosmological constant toward $0^+$. The adjustment is quantum-mechanical, discharging cosmological constant in random discrete steps. It renders de Sitter space unstable, and triggers its decay toward Minkowski. Since the instability dynamically stops at $\Lambda = 0$, the evolution favors the terminal Minkowski space without a need for anthropics. The mechanism works for any QFT coupled to gravity.

It is widely acknowledged that quantum mechanics may have profound philosophical implications, but what those implications are has been debated for nearly a century. The question addressed in this chapter is whether it has any implications that touch upon the truths of Christian revelation. The short answer is that quantum mechanics does not say anything directly about revealed truths but does have implications relevant to certain philosophical truths that the Church regards as entailed by Christian revelation. These include the truths that human beings have free will and that human beings are...

Of quantum physics, quantum chemistry and quantum mechanics, the latter is least useful for both chemical education and the practice of chemistry as a science concerned with the reactions and properties of chemical substances. We show that quantum mechanics must be viewed as a collection of methods, numbering at least thirteen, that one might apply for calculations on a system of an atomic scale. Instead of quantum mechanics we advocate the quantum laws or laws of discreteness, which have simple roots in laws of conservation and which have practical applications in various areas of obser...

The paper interprets the concept “operator in the separable complex Hilbert space” (particalry, “Hermitian operator” as “quantity” is defined in the “classical” quantum mechanics) by that of “quantum information”. As far as wave function is the characteristic function of the probability (density) distribution for all possible values of a certain quantity to be measured, the definition of quantity in quantum mechanics means any unitary change of the probability (density) distribution. It can be represented as a particular case of “unitary” qubits. The converse interpretation of any qubits as re...

There are several definitions of energy density in quantum mechanics. These yield expressions that differ locally, but all satisfy a continuity equation and integrate to the value of the expected energy of the system under consideration. Thus, the question of whether there are physical grounds to choose one definition over another arises naturally. In this work, we propose a way to probe a system by varying the size of a well containing a quantum particle. We show that the mean work done by moving the wall is closely related to one of the definitions for energy density. Specifically, the appro...

An example of non-Markovian quantum dynamics is considered in the framework of a geometrical (topological) subordination approach. The specific property of the model is that it coincides exactly with the fractional diffusion equation, which describes the geometric Brownian motion on combs. Both classical diffusion and quantum dynamics are described using the dilatation operator xddx. Two examples of geometrical subordinators are considered. The first one is the Gaussian function, which is due to the comb geometry. For the quantum consideration with a specific choice of the initial conditions, ...

Quantum mechanics is one of the most successful theories in science, and is relevant to nearly all modern topics of scientific research. This textbook moves beyond the introductory and intermediate principles of quantum mechanics frequently covered in undergraduate and graduate courses, presenting in-depth coverage of many more exciting and advanced topics. The author provides a clearly structured text for advanced students, graduates and researchers looking to deepen their knowledge of theoretical quantum mechanics. The book opens with a brief introduction covering key concepts and mathematic...

The author discusses the Spacetime Approach to Quantum Mechanics, in the context of the quantum field theory of closed systems, by generalising the sum-over-histories quantum mechanics formulation to deal with spacetime alternatives that are not at definite moments in time.

Reconstructing quantum mechanics has been an exploratory direction for physicists. Based on logical structure and basic principles of quantum mechanics, we propose a new method on reconstruction quantum mechanics completely by the waveparticle duality. This is divided into two steps: First, from wave form and duality we obtain the extensive quantum theory, which has the same quantum formulations only with different quantum constants H; then microscopic phenomena determine H=h. Further, we derive the corresponding commutation relation, the uncertainty principle and Heisenberg equation, etc. The...

Significance Conservation laws are some of the most important laws of physics. Having their origin in the symmetries of nature, conservation laws are present in all our physical theories. There are, however, significant differences between what conservation laws mean in these various theories. In quantum mechanics, which is a theory that is nondeterministic at a fundamental level, the conservation laws, as they are standardly formulated, do not refer to individual experiments but only to the statistics over a large ensemble of repeated identical experiments. Here, we take a step toward extendi...

An extension of IIT’s latest formalism is presented to evaluate the mechanism integrated information of a system subset to discrete, finite-dimensional quantum systems (e.g., quantum logic gates) and extend the notion of conditional independence to accommodate quantum entanglement.

It is shown that quantum mechanics predicts that the fidelity of the procedure decays exponentially with circuit depth, while EmQM predicts thatThe fidelity will decay significantly more rapidly for sufficiently deep circuits, which is the experimental signature that is proposed to search for.

This is a short note to answer Lawrence, Markiewicz and ´Zukowski objection [see arXiv:2108.11793] to Rovelli’s theory and concerning non-contextuality.

We derive the basic postulates of quantum physics from a few very simple operational assumptions based exclusively on the relative frequencies of observable events (measurement operations and measurement outcomes). We isolate a notion which can be identified with the system's own state, in the sense that it characterizes the system's probabilistic behavior against all possible measurement operations. We investigate some important features of the possible states of the system. All those investigations remain within the framework of classical Kolmogorovian probability theory, meaning that any ph...

Quantum Mechanics (QM) stands alone as a (very) successful physical theory, but the meaning of its variables and the status of many quantities in the mathematical formalism is obscure. This unique situation prompted the need for attribution of a physical meaning to the latter, a procedure known as interpretation. On the other hand, the study of QM is usually presented, even to future scientists, within the only framework developed by Bohr and the Copenhagen researchers, known as the Copenhagen interpretation. As a contribution to the understanding and teaching of Quantum Mechanics, aimed to a ...

One of the most famous metaphysical problems in the philosophy of quantum mechanics concerns the individuality status of quantum entities: are they individuals, or non-individuals? The typical approach to the problem consists in defending one of the options by appealing directly to features of quantum mechanics with the addition, eventually, of theoretical virtues the favoured proposal may have. In this paper, we argue that this strategy is inappropriate, because the problem of individuality is ill formulated in the case of quantum mechanics. In a nutshell, our point is that considerations exc...

The notorious `measurement problem' has been roving around quantum mechanics for nearly a century since its inception, and has given rise to a variety of `interpretations' of quantum mechanics, which are meant to evade it. We argue that no less than six problems need to be distinguished, and that several of them classify as different types of problems. One of them is what traditionally is called `the measurement problem' (here: the Reality Problem of Measurement Outcomes). Another of them has nothing to do with measurements but is a profound metaphysical problem. We also analyse critically Mau...

Quantum Mechanics in Nanoscience and Engineering covers both elementary and advanced quantum mechanics within a coherent and self-contained framework. Undergraduate students of physics, chemistry and engineering will find comprehensive coverage of their introductory quantum mechanics courses, and graduate students will gain an understanding of additional tools and concepts necessary to describe real world phenomena. Each topic presented is first motivated by an experimental technique, phenomenon or concept derived directly from the realm of nanoscience and technology. The machinery of quantum ...

An analysis of the quantum measurement problem is presented which is a modest modification of the standard one often called the Copenhagen interpretation, and finds that the outcomes of experiments can be considered factual data, and random in a classical sense.

Quantum mechanics does not provide any ready recipe for defining energy density in space, since the energy and coordinate do not commute. To find a well-motivated energy density, we start from a possibly fundamental, relativistic description for a spin-12 particle: Dirac's equation. Employing its energy-momentum tensor and going to the non-relativistic limit we find a locally conserved non-relativistic energy density that is defined via the Terletsky-Margenau-Hill quasiprobability (which is hence selected among other options). It coincides with the weak value of energy, and also with the hydro...

Long-lived mechanical oscillators are actively pursued as critical resources for quantum storage, sensing, and transduction. However, achieving deterministic quantum control while limiting mechanical dissipation remains a persistent challenge. Here, we demonstrate strong coupling between a transmon superconducting qubit and an ultra-long-lived nanomechanical oscillator ($T_\text{1} \approx 25 \text{ ms}$ at 5 GHz, $Q \approx 0.8 \times 10^9$) by leveraging the low acoustic loss in silicon and phononic bandgap engineering. The qubit-oscillator system achieves large cooperativity ($C_{T_1}\appro...

A quantum network consisting of magnonic and mechanical nodes connected by light is proposed. Recent years have witnessed a significant development in cavity magnonics based on collective spin excitations in ferrimagnetic crystals, such as yttrium iron garnet (YIG). Magnonic systems are considered to be a promising building block for a future quantum network. However, a major limitation of the system is that the coherence time of the magnon excitations is limited by their intrinsic loss (typically in the order of 1 μs for YIG). Here, we show that by coupling the magnonic system to a mechanical...

An overview of quantum mechanics in phase space is presented, and the formulation to generate a generalized phase-space function for any arbitrary quantum system is shown, such as the Wigner and Weyl functions along with the Q and P functions.

We propose a quantum mechanical theory of quantum spaces described by large $N$ noncommutative geometry as a model for quantum gravity. The theory admits fuzzy sphere as static solution. Over the fuzzy geometry, the quantum mechanics of the fermions is given by a sum of oscillators with equal frequency. The energy state where exactly half of the Fermi sea is filled contains the maximal amount of degeneracy. This state of the fuzzy sphere obeys the mass-radius relation of a Schwarzschild black hole if the fuzzy sphere is identified with the black hole horizon. Moreover the set of states in the ...

Pairs of pressures and velocities fields with kinetic energies are defined for quantum mechanical many-body systems, depending on the probability distribution and phase of a wavefunction. These functions satisfy a set of two classical energy-equations that is equivalent to the many-body time-dependent Schr¨odinger equation, and these equations also define two energy fields. An Euler equation of fluid dynamics is also derived that is satisfied by the fields. Interpretation of the Bohmian potential and the integrand of the expectation value of the kinetic energy is given, involving both pressure and cl...