Quantum Statistical Mechanics Research Articles

Obtaining the molar heat capacities and entropies of HCl and HBr by combining density functional theory and machine learning algorithm

AbstractAn integrated approach combing density functional theory (DFT) and machine learning algorithm (MLA) is proposed here to obtain the molar heat capacities and entropies of diatomic macroscopic gasses with high quality. The DFT approach takes care of the main physical effects, while machine learning takes care of the intricate details it leaves out. After machine learning algorithm correction, a complete set of accurate prediction of vibrational energy spectrum is obtained, which is better than the results of DFT methods in accuracy. And then it is used to replace the vibrational part in the ro‐vibrational energy calculated by DFT to obtain the rectified ro‐vibrational energy. Furthermore, through the quantum ensemble theory, the thermodynamic properties of the macroscopic gas are calculated by the predicted ro‐vibrational energy spectrum, and are modified again by the machine learning algorithm. The study of the and system show that, compared with CCSD(T)/cc‐pV5Z and the improved variational algebraical method, the macroscopic thermodynamic properties calculated by this work in the temperature range of 300–6000 K are the closest to the experimental values. The relative error is less than 1% at each temperature.

The Renormalization Group

The renormalization group was originally introduced as a multiscale approach to quantum field theory and the theory of critical phenomena, explaining in particular the universality observed e.g. in critical exponents. Over the years it has become a powerful tool in the mathematical analysis of systems with infinitely many interacting degrees of freedom. Its applications include quantum field theories, classical and quantum statistical mechanics, (stochastic) partial differential equations, operator theory, and probability theory. For some important problems, it is the only known tool for mathematical proofs. The last few years have seen further important developments, in particular in the application of the method to probabilistic questions, and to equilibrium and non-equilibrium quantum statistical mechanics. This workshop has given an account of the most important new developments in the last five years, including methodical progress, current applications, relations to other approaches, and identified new challenges that may be tackled in future work with the help of the renormalization group.

Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices

The study of non-equilibrium dynamics is one of the most important challenges of modern quantum many-body physics, in relationship with fundamental questions in quantum statistical mechanics, as well as with the fields of quantum simulation and computing. In this work we propose a Gaussian Ansatz for the study of the nonequilibrium dynamics of quantum spin systems. Within our approach, the quantum spins are mapped onto Holstein-Primakoff bosons, such that a coherent spin state - chosen as the initial state of the dynamics - represents the bosonic vacuum. The state of the system is then postulated to remain a bosonic Gaussian state at all times, an assumption which is exact when the bosonic Hamiltonian is quadratic; and which is justified in the case of a nonlinear Hamiltonian if the boson density remains moderate. We test the accuracy of such an Ansatz in the paradigmatic case of the S=1/2S=1/2 transverse-field Ising model, in one and two dimensions, initialized in a state aligned with the applied field. We show that the Gaussian Ansatz, when applied to the bosonic Hamiltonian with nonlinearities truncated to quartic order, is able to reproduce faithfully the evolution of the state, including its relaxation to the equilibrium regime, for fields larger than the critical field for the paramagnetic-ferromagnetic transition in the ground state. In particular the spatio-temporal pattern of correlations reconstructed via the Gaussian Ansatz reveals the dispersion relation of quasiparticle excitations, exhibiting the softening of the excitation gap upon approaching the critical field. Our results suggest that the Gaussian Ansatz correctly captures the essential effects of nonlinearities in quantum spin dynamics; and that it can be applied to the study of fundamental phenomena such as quantum thermalization and its breakdown.

Unique solvent effect of water in radical cyclization reaction

The radical cyclization reaction in the aqueous environment by Yorimitsu et al. is revisited using the RISM-SCF-cSED method, a hybrid of quantum chemistry and statistical mechanics theory for molecular liquids. The difference between the barrier height of the forward reaction from the intermediate E-rot, the cyclization step, and that of the backward reaction is crucial to the reaction yield. Considering the effect of hydrogen bonding through the RISM theory, we found that the barrier height for the forward reaction is lower, especially in water. In other words, considering microscopic solvation effects clearly shows the difference between water and DMSO solvents, explaining the remarkable acceleration of the reaction in the aqueous environment.

Relaxation of Multitime Statistics in Quantum Systems

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate.

Quantum dynamical effects of vibrational strong coupling in chemical reactivity

Recent experiments suggest that ground state chemical reactivity can be modified when placing molecular systems inside infrared cavities where molecular vibrations are strongly coupled to electromagnetic radiation. This phenomenon lacks a firm theoretical explanation. Here, we employ an exact quantum dynamics approach to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

Numerical Aspects of Resonant States in Quantum Mechanics

Numerical Aspects of Resonant States in Quantum Mechanics

The Standard Model and quantum state reduction from Heim’s field theory

Abstract Core parts of the Standard Model are derived from B. Heim’s quantum field theory, whose poly-metric describes spacetime and matter in a unified formalism. Its non-linear eigenvalue equation transforms into the Einstein field equation in the macroscopic limit. The 6-dimensional Heim space can be determined as locally isomorphic to a SU(2) ⊗ SU(2) ⊗ U(1) ⊗ U(1) symmetry and thus to the SU(3), which allows to connect to the local gauge symmetries and boson fields of the Standard Model. The Fermion and Higgs field and their coupling are deduced from Heim’s basic equations, providing new insight into possible correlations of these fields. Furthermore, the derivation yields an additional imaginary coupling term which seems to account for quantum mechanical state reduction in the non-relativistic limit. The recently performed calculation of the mass spectrum of elementary particles in a new approach based on Heim’s theory (with average error to the data < 1 % ${< } 1\%$ ) appears as even more relevant, having now shown that the theory can connect to the achievements of the Standard Model.

Quantum statistical mechanics of dissolving Abelian Higgs vortices

The quantum partition function for Abelian Higgs vortices at high density—the regime of dissolving vortices—is calculated explicitly, using spectral data for the Beltrami Laplacian on the N-vortex moduli space with a scaled Fubini–Study metric. From the partition function, the pressure of the vortex gas is derived. There are three asymptotic regimes—High, Intermediate and Low Temperature. The phase crossover from Intermediate to Low Temperature is modelled by a Bessel function. In the Low Temperature regime the free energy is not extensive but is proportional to N 2.

Parameter-free prediction of phase transition in PbTiO3 through combination of quantum mechanics and statistical mechanics

Thermodynamics of ferroelectric materials and their ferroelectric to paraelectric (FE-PE) transitions is commonly described by the phenomenological Landau theory and more recently by effective Hamiltonian and various potentials, all with model parameters fitted to experimental or theoretical data. Here we show that the zentropy theory, which considers the total entropy of a system as a weighted sum of entropies of configurations that the system may experience and the statistical entropy among the configurations, can predict the FE-PE transition without fitting parameters. For PbTiO3, the configurations are identified as the FE configurations with 90- or 180° domain walls in addition to the ground state FE configuration without domain wall. With the domain wall energies predicted from first-principles based on density functional theory in the literature as the only inputs, the FE-PE transition for PbTiO3 is predicted showing remarkable agreement with experiments, unveiling the microscopic fundamentals of the transition.

Tracer or toxicant: Does stable isotope labeling affect central processes in aquatic food webs?

Stable isotope analysis (SIA) is an elementary technique in food web ecology, but its insights become increasingly ambiguous in complex systems. One approach to elevate the utility of SIA in such systems is the use of heavy isotope tracers (i.e., labeling). However, the fundamental assumption that the addition of such tracers does not affect in situ conditions has been challenged. This study tests if labeling is suitable for autotrophy-based and detritus-based aquatic food webs. For the former, the survival and reproduction of Daphnia magna fed with phytoplankton cultured at different levels of 15N addition were assessed. For the latter, the microbial decomposition of leaf litter was assessed at the same tracer levels. While no significant differences were observed, effect patterns were comparable to a previous study, supporting the isotopic redundancy hypothesis that postulates discrete quantum mechanical states at which the reaction speeds of metabolic processes are altered. Although physiology (reproduction) and activity (microbial decomposition) might not be altered to an ecologically significant level, labeling with heavy stable isotopes could potentially affect isotopic fractionation in biochemical processes and bias conclusions drawn from resulting SI ratios.

Quantum statistical mechanics near a black hole horizon

We undertake a first-principles analysis of the thermodynamics of a small body near a black hole horizon. In particular, we study the paradigmatic system of a quantum ideal gas in a small box hovering over the Schwarzschild horizon. We describe the gas in terms of free quantum fields, bosonic and fermionic, massive and massless. We identify thermodynamic properties through the microcanonical distribution. We first analyse the more general case of a box in Rindler spacetime, and then specialize to the black hole case. The physics depends strongly on the distance of the box from the horizon, which we treat as a macroscopic thermodynamic variable. We find that the effective dimension of the system transitions from three-dimensional to two-dimensional as we approach the horizon, that Bekenstein's bound fails when the box is adiabatically lowered towards the black hole, and that the pressure is highly anisotropic. The pressure difference between the upper and lower wall leads to an effective force that must be added to the gravitational acceleration. We also show that the approximation of quantum fields propagating on a fixed background for matter breaks down when the system is brought to microscopic distances from the horizon, in which case backreaction effects must be included.

Hybrid accurate simulations for constructing some novel analytical and numerical solutions of three-order GNLS equation

This study presents analytical and numerical solutions of a simplified third-order generalized nonlinear Schrödinger equation (GNLSE) to demonstrate how ultrashort pulses behave in optical fiber and quantum fields. The investigated model can be used as a wave model to illustrate the wave aspect of the matter. It is called a quantum-mechanical state function because it might show how atoms and transistors move and act physically. Four analytical and numerical schemes are used to construct an accurate novel solution. Khater II (Kha II) and novel Kudryashov (NKud) methods are present in the employed analytical scheme. In contrast, the exponential cubic-B-spline and trigonometric-quantic-B-spline schemes represent the simulated numerical techniques. Many novel solitary wave solutions are constructed and formulated in some distinct forms and represented through density, three-, and two-dimensional graphs. The built analytical solutions accuracy is investigated by deriving the requested boundary and initial conditions for implementing the suggested numerical schemes that show the matching between both solutions (analytical and numerical). This matching between solutions proves the accuracy of the obtained solutions. Additionally, to guarantee the applicability of our solutions, we investigate their stability by using the Hamiltonian systems properties. Finally, the novelty of our study and its scientific contributions are illuminated by comparing our results with recently published ones.

Theoretical Understanding of the Nonlinear Raman Shift of C≡N Stretching Vibration of p-Aminobenzonitrile in Supercritical Water.

Subcritical and supercritical fluids (SCF) have attracted significant attention in the past few decades because of their unique properties. In a previous study, a nonlinear Raman shift of the C≡N stretching vibration of p-aminobenzonitrile (p-ABN) with respect to the supercritical water (SCW) density was observed [K. Osawa et al., J. Phys. Chem. A 2009, 113, 3143-3154]. Although a plausible mechanism of the nonlinear Raman shift was proposed in the study, the discussion at the atomistic level was inadequate. To elucidate the nonlinear Raman shift mechanism of the C≡N stretching vibration of p-ABN in SCW from a theoretical viewpoint, we employed RISM-SCF-cSED, which is the hybrid method between quantum mechanics and statistical mechanics. We discovered that the hydrogen-bonding effect is dominant at low- and middle-density regions, while the packing effect is dominant at the high-density region. The balances of these effects determine the Raman shift of p-ABN in SCF.

Approach to Equilibrium in Translation-Invariant Quantum Systems: Some Structural Results

We formulate the problem of approach to equilibrium in algebraic quantum statistical mechanics and study some of its structural aspects, focusing on the relation between the zeroth law of thermodynamics (approach to equilibrium) and the second law (increase in entropy). Our main result is that approach to equilibrium is necessarily accompanied by a strict increase in the specific (mean) energy and entropy. In the course of our analysis, we introduce the concept of quantum weak Gibbs state which is of independent interest.

Selective quantum ensemble learning inspired by improved AdaBoost based on local sample information

In ensemble learning, random subspace technology not only easily loses some important features but also easily produces some redundant subspaces, inevitably leading to the decline of ensemble learning performance. In order to overcome the shortcomings, we propose a new selective quantum ensemble learning model inspired by improved AdaBoost based on local sample information (SELA). Firstly, SELA combines information entropy and random subspace to ensure that the important features of the classification task in each subspace are preserved. Then, we select the base classifier that can balance accuracy and diversity among a group of base classifiers generated based on local AdaBoost in each iteration. Finally, we utilize the quantum genetic algorithm to search optimal weights for base learners in the label prediction process. We use UCI datasets to analyze the impact of important parameters in SELA on classification performance and verify that SELA is usually superior to other competitive algorithms.

Bound on quantum fluctuations in gravitational waves from LIGO-Virgo

We derive some of the central equations governing quantum fluctuations in gravitational waves, making use of general relativity as a sensible effective quantum theory at large distances. We begin with a review of classical gravitational waves in general relativity, including the energy in each mode. We then form the quantum ground state and coherent state, before then obtaining an explicit class of squeezed states. Since existing gravitational wave detections arise from merging black holes, and since the quantum nature of black holes remains puzzling, one can be open-minded to the possibility that the wave is in an interesting quantum mechanical state, such as a highly squeezed state. We compute the time and space two-point correlation functions for the quantized metric perturbations. We then constrain its amplitude with LIGO-Virgo observations. Using existing LIGO-Virgo data, we place a bound on the (exponential) squeezing parameter of the quantum gravitational wave state of ζ < 41.

On the Concept of State in Quantum Mechanics: Another Way to Decoherence?

On the Concept of State in Quantum Mechanics: Another Way to Decoherence?

QBoost for regression problems: solving partial differential equations

A hybrid algorithm based on machine learning and quantum ensemble learning is proposed to find an approximate solution to a partial differential equation with good precision and favorable scaling in the required number of qubits. The classical component consists in training several regressors (weak-learners), capable of solving a partial differential equation approximately using machine learning. The quantum component consists in adapting the QBoost algorithm to solve regression problems to build an ensemble of classical learners. We have successfully applied our framework to solve the 1D Burgers’ equation with viscosity, showing that the quantum ensemble method really improves the solutions produced by classical weak-learners. We also implemented the algorithm on the D-Wave Systems, confirming the good performance of the quantum solution compared to the simulated annealing and exact solver methods.

Creating large Fock states and massively squeezed states in optics using systems with nonlinear bound states in the continuum

The quantization of the electromagnetic field leads directly to the existence of quantum mechanical states, called Fock states, with an exact integer number of photons. Despite these fundamental states being long-understood, and despite their many potential applications, generating them is largely an open problem. For example, at optical frequencies, it is challenging to deterministically generate Fock states of order two and beyond. Here, we predict the existence of an effect in nonlinear optics, which enables the deterministic generation of large Fock states at arbitrary frequencies. The effect, which we call an n-photon bound state in the continuum, is one in which a photonic resonance (such as a cavity mode) becomes lossless when a precise number of photons n is inside the resonance. Based on analytical theory and numerical simulations, we show that these bound states enable a remarkable phenomenon in which a coherent state of light, when injected into a system supporting this bound state, can spontaneously evolve into a Fock state of a controllable photon number. This effect is also directly applicable for creating (highly) squeezed states of light, whose photon number fluctuations are (far) below the value expected from classical physics (i.e., shot noise). We suggest several examples of systems to experimentally realize the effects predicted here in nonlinear nanophotonic systems, showing examples of generating both optical Fock states with large n (n > 10), as well as more macroscopic photonic states with very large squeezing, with over 90% less noise (10 dB) than the classical value associated with shot noise.