Quantum Statistical Mechanics Research Articles

Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications.

Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical states, and not yet explained. The concept of "statistical balance" is here explored, comparing its meaning since 2019 with its original meaning in 2001. Statistical balance now refers to a feature of contexts in which: (a) there is a prescribed probability other than 0 or 1 for the collective response of an ensemble to one measurement type; and (b) the collective response of the same ensemble to another measurement type demonstrates that no well-defined value can be attributed, for the property relevant to the original measurement type, to individual members of the ensemble. In some unexplained way, the outcomes of single runs of a measurement of the original type "balance" each other to give an overall result in line with the prescribed probability. Unexplained statistical balance prompts caution in assessing the conceptual implications of entanglement, measurement, uncertainty, and two-slit and Bell-type analyses. Physicists have a responsibility to the wider population to be conceptually precise about quantum mechanics, and to make clear that many possible conceptual implications are uncertain.

Gravitational fields and quantum mechanics

Massive particles in spatially nonlocal, quantum mechanical wave functions should have interesting gravitational fields. Should their gravitational fields be classical? What aspects of their gravitational fields are observable? We study these questions using quantum field theory to gravitationally probe the wave functions of such quantum mechanical states. We find that the observable signals seem to indicate that it is very difficult to phenomenologically observe the quantum mechanical, spatially nonlocal superposition.

Flood Susceptibility Mapping Using Novel Hybrid Approach of Neural Network with Genetic Quantum Ensembles

Flood susceptibility mapping is an important method for flood research. In this paper, we combine a backpropagation neural network (BPNN) with a genetic quantum algorithm (GQA) for the first time to develop flood susceptibility mapping. The area on the Chinese side of the Tumen River Basin was selected as the research object. A set of flood conditioning factors was selected based on relevant literature and an actual situation and then validated using the chi-square test and correlation analysis. Different weights were assigned using stepwise weight assessment ratio analysis. Finally, modeling and flood susceptibility mapping using GQA-BPNN. As a reference, the same work was performed with both the pure BPNN and optimized BPNN using a genetic algorithm (GA). The results show that the area under the curve, root mean squared error, Nash-Sutcliffe coefficient and percentage of bias are significantly better for the GQA-BPNN than for the BPNN and GA-BPNN and that the flood sensitivity maps constructed by the GQA-BPNN have more flood points in high flood sensitivity areas. Therefore, the GQA-BPNN method can be considered an effective method for flood susceptibility mapping.

Bose–Einstein condensation of two-dimensional spin-1 Cooper pairs in a uniform magnetic field

Bose–Einstein condensation of two-dimensional spin-1 Cooper pairs in a uniform magnetic field is investigated within the framework of quantum statistical mechanics. We derive an exact analytical solution of two-dimensional spin-1 Cooper pairs in a uniform magnetic field, which involves a q-digamma function in mathematics. In two dimensions, it is found that the critical temperature and condensate fraction are monotonically increasing functions of magnetic field B, Landé factor g, and number density σ. Our investigation in two dimensions provides an example of the magnetic-field-tuned insulator-superconductor quantum phase transition.

Waving arms around to teach quantum mechanics

Kinesthetic (or embodied) representations help students build intuition and deep understanding of concepts. This paper presents a series of kinesthetic activities for a spins-first undergraduate quantum mechanics course that supports students in reasoning and developing intuition about the complex-valued vectors of spin states. The arms representation, used in these activities, was developed as a tangible representation of complex numbers: Students act as an Argand diagram, using their left arm to represent numbers in the complex plane. The arms representation is versatile and can be expanded to depict complex-valued vectors with groups of students. This expansion enables groups of students to represent quantum mechanical state vectors with their arms. We have developed activities using the arms representation that parallel the progression of a spins-first approach by starting with complex numbers, then representing two- and three-state systems, considering time-dependence, and, eventually, extending to approximate wavefunctions. Each activity illustrates the complex nature of quantum states and provides a tangible manipulative from which students can build intuition about quantum phenomena.

Integration of Quantum Chemistry, Statistical Mechanics, and Artificial Intelligence for Computational Spectroscopy: The UV-Vis Spectrum of TEMPO Radical in Different Solvents.

The ongoing integration of quantum chemistry, statistical mechanics, and artificial intelligence is paving the route toward more effective and accurate strategies for the investigation of the spectroscopic properties of medium-to-large size chromophores in condensed phases. In this context we are developing a novel workflow aimed at improving the generality, reliability, and ease of use of the available computational tools. In this paper we report our latest developments with specific reference to unsupervised atomistic simulations employing non periodic boundary conditions (NPBC) followed by clustering of the trajectories employing optimized feature spaces. Next accurate variational computations are performed for a representative point of each cluster, whereas intracluster fluctuations are taken into account by a cheap yet reliable perturbative approach. A number of methodological improvements have been introduced including, e.g., more realistic reaction field effects at the outer boundary of the simulation sphere, automatic definition of the feature space by continuous perception of solute–solvent interactions, full account of polarization and charge transfer in the first solvation shell, and inclusion of vibronic contributions. After its validation, this new approach has been applied to the challenging case of solvatochromic effects on the UV–vis spectra of a prototypical nitroxide radical (TEMPO) in different solvents. The reliability, effectiveness, and robustness of the new platform is demonstrated by the remarkable agreement with experiment of the results obtained through an unsupervised approach characterized by a strongly reduced computational cost as compared to that of conventional quantum mechanics and molecular mechanics models without any accuracy reduction.

Observation of Bose-Einstein condensates of excitons in a bulk semiconductor

An unambiguous observation of the Bose-Einstein condensation (BEC) of excitons in a photoexcited bulk semiconductor and elucidation of its inherent nature have been longstanding problems in condensed matter physics. Here, we observe the quantum phase transition and a Bose-Einstein condensate appearing in a trapped gas of 1s paraexcitons in bulk Cu2O below 400 mK, by directly visualizing the exciton cloud in real space using mid-infrared induced absorption imaging that we realized in a dilution refrigerator. Our study shows that the paraexciton condensate is undetectable by conventional luminescence spectroscopy. We find an unconventionally small condensate fraction of 0.016 with the spatial profile of the condensate well described by mean-field theory. Our discovery of this new type of BEC in the purely matter-like exciton system interacting with a cold phonon bath could pave the way for the classification of its long-range order, and for essential understanding of quantum statistical mechanics of non-equilibrium open systems.

Foundations of Quantum Computing: II. The Many Faces of ‎Quantum Uncertainty

In this Part II we focus on a few key elements of quantum mechanics essential for understanding of quantum technologies ‎and computing. We begin with a subtle but important similarity between classical and quantum mechanics which is typically ‎overlooked in favor of apparent differences. Further, it is reminded that classical motion can be obtained via averaging ‎over quantum distributions/wave functions and, conversely, quantum distributions can be recast as a superposition of virtual ‎classical paths. Relatedly, we emphasize the importance of the case intermediate between classical and quantum mechanics – ‎that is, quasi-classical mechanics. The above background facilitates additional insights and heuristics into the mechanisms of ‎widely acclaimed long-distance correlations in quantum mechanics and the origins of the coherency in quantum ensembles in the ‎context of wave-particle duality. ‎

Step-by-step state-selective tracking of fragmentation dynamics of water dications by momentum imaging

The double photoionization of a molecule by one photon ejects two electrons and typically creates an unstable dication. Observing the subsequent fragmentation products in coincidence can reveal a surprisingly detailed picture of the dynamics. Determining the time evolution and quantum mechanical states involved leads to deeper understanding of molecular dynamics. Here in a combined experimental and theoretical study, we unambiguously separate the sequential breakup via D+ + OD+ intermediates, from other processes leading to the same D+ + D+ + O final products of double ionization of water by a single photon. Moreover, we experimentally identify, separate, and follow step by step, two pathways involving the b 1Σ+ and a 1Δ electronic states of the intermediate OD+ ion. Our classical trajectory calculations on the relevant potential energy surfaces reproduce well the measured data and, combined with the experiment, enable the determination of the internal energy and angular momentum distribution of the OD+ intermediate.

Foundations of Quantum Computing: I-Demystifying ‎‎Quantum Paradoxes

Speedy developments in Quantum Technologies mandate that fundamentals of Quantum Computing are well explained and ‎understood. Meanwhile, paradigms of so-called quantum non-locality, wave function (WF) “collapse”, “Schrödinger cat” and ‎some other historically popular misconceptions continue to feed mysteries around quantum phenomena. Arguing that above ‎misinterpretations stem from classically minded and experimentally unverifiable perceptions, recasting Principle of ‎Superposition (PS) and key experimental details into classical notions. Revisiting main components of general quantum ‎measurement protocols (analyzers and detectors), and explaining paradoxes of WF collapse and Schrödinger cat. Reminding ‎that quantum measurements routinely reveal correlations dictated by conservation laws in each individual realization of the ‎quantum ensemble, manifesting “correlation-by-initial conditions” in contrast to traditional “correlation-by-interactions”. We ‎reiterate: Quantum Mechanics (QM) is not a dynamical theory in the same sense the Classical Mechanics (CM) is – it is a ‎statistical phenomenology, as established in 1926 by Born’s postulate. That is, while QM rests on conservation laws in each ‎individual outcome, it does not indicate how exactly a specific outcome is selected. This selection remains fundamentally ‎random and represents true randomness of QM, the latter being a statistical paradigm with a WF standing for a complex-‎valued distribution function. Finally, PS is the backbone of a quantum measurement process: PS can be conveniently viewed ‎as a composition of partial distributions into the total distribution – similar to classical probability mixtures – and is ‎effectuated experimentally by the analyzer part of a measuring device. ‎

Quantum statistical mechanics of encryption: Reaching the speed limit of classical block ciphers

We cast encryption via classical block ciphers in terms of operator spreading in a dual space of Pauli strings, a formulation which allows us to characterize classical ciphers by using tools well known in the analysis of quantum many-body systems. We connect plaintext and ciphertext attacks to out-of-time order correlators (OTOCs) and quantify the quality of ciphers using measures of delocalization in string space such as participation ratios and corresponding entropies obtained from the wave function amplitudes in string space. In particular, we show that in Feistel ciphers the entropy saturates its bound to exponential precision for ciphers with 4 or more rounds, consistent with the classic Luby–Rackoff result that it takes these many rounds to generate strong pseudorandom permutations. The saturation of the string-space information entropy and the vanishing of the OTOCs to exponential precision are taken as necessary conditions for the security of the cipher — we conjecture these criteria are also sufficient, as physically they signal irreversibility and chaos. We argue that the conditions on both OTOCs and string entropies can be satisfied by n-bit block ciphers implemented via random reversible circuits with O(nlogn) gates. This paper focuses on a tree-structured cipher composed of layers of n/3 3-bit gates, for which a “key” specifies uniquely the sequence of gates that comprise the circuit. We show that in order to reach this “speed limit” one must employ a three-stage circuit consisting of a nonlinear stage implemented by layers of nonlinear gates that proliferate the number of strings, flanked by two linear stages, each deploying layers of a special set of linear “inflationary” gates that accelerate the growth of small individual strings. The close formal correspondence to quantum scramblers established in this work leads us to suggest that this three-stage construction is also required in order to scramble quantum states to similar precision and with circuits of similar size. A shallow, O(logn)-depth cipher of the type described here can be used in constructing a polynomial-overhead scheme for computation on encrypted data proposed in another publication as an alternative to Homomorphic Encryption.

Coarse-Graining of Imaginary Time Feynman Path Integrals: Inclusion of Intramolecular Interactions and Bottom-up Force-Matching.

Feynman's imaginary time path integral formalism of quantum statistical mechanics and the corresponding quantum-classical isomorphism provide a tangible way of incorporating nuclear quantum effect (NQE) in the simulation of condensed matter systems using well-developed classical simulation techniques. Our previous work has presented the many-body coarse-graining of path integral (CG-PI) theory that builds an isomorphism between the quantum partition function of N distinguishable particles and the classical partition function of 2N pseudoparticles. In this present work, we develop a generalized version of the many-body CG-PI theory that incorporates many-body interactions in the force field. Based on the new derivation, we provide a numerical CG-PI (n-CG-PI) modeling strategy parametrized from the underlying path integral molecular dynamics (PIMD) trajectories using force matching and Boltzmann inversion. The n-CG-PI models for two liquid systems are shown to capture well both the intramolecular and intermolecular structural correlations of the reference PIMD simulations. The generalized derivation of the many-body CG-PI theory and the n-CG-PI model presented in this work extend the scope of the CG-PI formalism by generalizing the previously limited theory to incorporate force fields of realistic molecular systems.

Schrödinger representation of quantum mechanics, Berry connection, and superconductivity

The standard quantum mechanical electronic state calculations for molecules and solids use the Schrödinger representation where the momentum conjugate to the coordinate qr is given by −iħ∂∂qr. This formalism contains an extra U(1) phase degree-of-freedom. We show that it can be regarded as a Berry phase arising from many-electron interaction, and when it is non-trivial, it gives rise to a current carrying ground state identified as the superconducting ground state. It is shown that this superconducting state is connected to the BCS one, and captures the experimentally verified results of the BCS theory. There are also gratifying differences that remove the shortcomings of the BCS theory; the ground state is particle-number-conserving, and the mass appearing in the London moment phenomenon is the free electron mass.

Spin and exchange in mixed quantum states from first principles in Feynman path integral quantum statistical mechanics representation

The exchange and space correlations in the system of indistinguishable electrons against the background of thermal fluctuations are studied from first principles. A complete set of mutually orthogonal spin-coordinate basis functions symmetric with respect to permutations in coordinate and spin variables is constructed by the action of Young symmetry operators. As an illustration of a general approach, Path Integral Monte Carlo (PIMC) computer simulation of mixed quantum states of four electrons in a model ellipsoidal nanoscopic trap with soft walls is performed. The equilibrium value of the spin is calculated as well as the mechanism of its formation depending on the temperature and shape of the trap in connection with the evolution of the spatial organization of electrons is analyzed. The Quantum-statistical calculation, executed with a fundamentally accurate description of the permutation symmetry of electrons and the spin variable, includes in explicit form the Coulomb and exchange correlations of all orders and the energy exchange with a thermal bath. The equilibrium values ​​of the spin in dependence of the shape of the potential well and temperature as well as statistical distributions over the eigenfunctions of the spin squared operator are obtained. A general, fundamentally accurate and numerically implementable on computers available today computers approach for describing the spin states of systems of different numbers of indistinguishable fermions with spin 1/2 in the representation of path integrals is formulated.The regularities in dependence of spin on the shape of the system and on the temperature are studied. The variations in the geometry of the trap in direction of elongated shapes are accompanied by the transfer of a part of the electron cloud first from the equator to the poles of the ellipsoidal potential well, and then in the opposite direction with the subsequent collapse of the ring-shaped form into a compact clot in the center and its decomposition into two fragments localized on the axis of rotation. The spin of the mixed quantum state of four electrons at room temperature varies depending on the geometry of the system in the opposite direction, compared with the system of two and three electrons, reaching its maximum at a spherical shape. Spin states of electron ensembles several nanometers in size are unstable to thermal perturbations already in the region of room temperatures. Compression leads to a stabilization of spin states. The calculation results indicate a strong dependence of the energy of collective mixed spin states of electrons on a detailed account of exchange and Coulomb high-orders spatial correlations.

Noncommutative phase-space Lotka-Volterra dynamics: The quantum analog.

The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics extended to one-dimensional Hamiltonian systems, H(x,k) constrained by the ∂^{2}H/∂x∂k=0 condition. Supported by the Heisenberg-Weyl noncommutative algebra, where [x,k]=i, the canonical variables x and k are interpreted in terms of the LV variables, y=e^{-x} and z=e^{-k}, eventually associated with the number of individuals in a closed competitive dynamics: the so-called prey-predator system. The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales and for quantifying quantum analog effects. Through the results from the associated Wigner currents, (non-)Liouvillian and stationary properties are described for thermodynamic and Gaussian quantum ensembles in order to account for the corrections due to quantum features over the classical phase-space pattern yielded by the Hamiltonian description of the LV dynamics. In particular, for Gaussian statistical ensembles, the Wigner flow framework provides the exact profile for the quantum modifications over the classical LV phase-space trajectories so that Gaussian quantum ensembles can be interpreted as an adequate Hilbert space state configuration for comparing quantum and classical regimes. The generality of the framework developed here extends the boundaries of the understanding of quantumlike effects on competitive microscopical biosystems.

An interpretation of quantum foundations based on density functional theory and polymer self-consistent field theory

The Feynman quantum-classical isomorphism between classical statistical mechanics in 3+1 dimensions and quantum statistical mechanics in 3 dimensions is used to connect classical polymer self-consistent field theory with quantum time-dependent density functional theory. This allows the theorems of density functional theory to relate non-relativistic quantum mechanics to a classical statistical mechanical derivation of polymer self-consistent field theory for ring polymers in a 4 dimensional thermal-space. One dynamic postulate is added to two static postulates which allows for a description of quantum physics from a 5 dimensional thermal-space-time ensemble perspective. A connection with aspects of classical field theory can be made in the classical limit.

Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin–orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.

Possible realization of the Majumdar-Ghosh point in the mineral szenicsite

The Majumder-Ghosh (MG) point is a point in parameter space for a one-dimensional (1D) frustrated system where $\ensuremath{\alpha}={J}_{1}/{J}_{2}=0.5$ and the ground state is shown to be a superposition of singlet states. This leads to no magnetic order, instead the ground state is dominated by electronic dynamics, much like that of a spin liquid. Szenicsite is a natural mineral that is predicted to have isolated 1D ${\mathrm{Cu}}^{2+}$ chains and lies close to or on the MG point. In this work we use muon spin spectroscopy to demonstrate that szenicsite does not magnetically order down to 100 mK and there is an absence of a spin gap, with 1D magnetic excitations dominating. Therefore, we believe szenicsite shows the properties that would put it on the MG point and, as such, it is an interesting system for studying the properties of this quantum mechanical state.

Towards quantum thermal multi-transistor systems: Energy divider formalism

A quantum thermal transistor controls the flow of thermal energy through two of its terminals in response to an external input signal on its third terminal. In recent years, several realizations of thermal transistors combining individual quantum systems have been proposed using temperatures or optical fields as the control signals. The success of the electronic transistor in modern technology partly lies in its ability to combine and make multi-transistor systems with enhanced flow control capability or even wholly different behaviors. Hence, as the next natural step, we investigate the intricacies of building composite systems combining multiple quantum thermal transistors. We identify that the interconnects of thermal transistors play a critical role in these systems by facilitating energy exchange from one transistor to another. By isolating the exact functionality of these interconnects, we develop a simple model that still captures all its essential characteristics. This model shows that directly coupling transistors allows a substantial energy transfer between them only under highly restrictive conditions. We then develop the energy divider formalism where a single properly tuned quantum harmonic oscillator acts as an intermediary between the transistors. We demonstrate that the oscillator mediates a substantial energy exchange under a considerably relaxed set of conditions and illustrate its operating principles through detailed quantum mechanical state analysis. We compare our energy divider based interconnect against the previously developed intermediate bath method and confirm that both ways achieve similar thermal energy flow rates between the transistors over a broad range of operating temperatures. At the same time, replacing an intermediate bath made up of a large number of harmonic oscillators with a single oscillator avoids many of the theoretical and practical limitations of the earlier method. For instance, time-domain simulations show that the energy divider based interconnect responds far faster to an external excitation than the corresponding intermediate bath based system. We believe the energy divider formalism provides valuable insights into the nature of thermal energy transfer within quantum thermal systems.

Nanodiamond islands confined between two graphene sheets as perspective 2D quantum materials

Based on direct space DFT PBE0/6-31G* electronic structure calculations, the structure and properties of nanodiamond islands confined between two finite graphene fragments (NDI-c2G) was proposed and theoretically explored. DFT simulations revealed that fusion of planar aromatic molecules with two parent graphene fragments may form either cubic or hexagonal allotropes of NDI-c2Gs lattices accompanied with formation of local corrugated sp3 sites with substituted dangling bonds embedded into graphene sublattices. It was shown that at the DFT level of theory, low distortion energies of NDI-c2Gs lattices are comparable or smaller than the energy of van-der-Waals interactions, which allows the NDI-c2G lattices to be stabilized by a support and finally synthesized. The Nuclear Independent Chemical Shift calculations, shows that in the vicinity of NDI regions, graphene lattices are estimated to be either low-, or anti-aromatic. Furthermore, the formation of NDI-c2Gs leads to localization of HOMO and LUMO states at different sites of the NDI-c2Gs lattices. The NDI-c2G regions with confined frontier orbitals can be considered as arrays of quantum dots isolated from each other by NDI scattering centres of 3.82 Å dimension. The results demonstrates that NDI-c2G should be considered as strongly-correlated entangled hybrid quantum dots which may form extended quantum ensembles with great potential for advanced quantum applications.