Quantum Statistical Theory Research Articles

Calculation of the Second EXAFS Cumulant of Si Using the Anharmonic Correlated Einstein Model

The second expanded X-ray absorption fine structure (EXAFS) cumulant of the crystalline silicon (Si) has been studied in the temperature-dependent. This is calculated in explicit forms using the anharmonic correlated Einstein (ACE) model developed from the correlated Einstein model based on the anharmonic effective potential and the quantum statistical theory. The numerical results of Si in the temperature range from 0 to 1200 K are in good agreement with those obtained by the other theoretical models and experiments at several temperatures. The analytical results show that the ACE model is suitable for analyzing the experimental EXAFS data of diamond cubics.

Investigating Anharmonic XAFS Debye-Waller Factor of Crystalline Tungsten Based on Einstein Model

The anharmonic X-ray absorption fine structure (XAFS) Debye-Waller (DW) factor of the crystalline tungsten (W) has been investigated in the temperature-dependent. This DW factor is calculated in explicit forms using the quantum anharmonic correlated Einstein model developed from the correlated Einstein model based on the anharmonic effective potential and the quantum statistical theory. The numerical results of W in the temperature range from 0 to 900 K are in good agreement with those obtained by the other theoretical models and experiments at several temperatures. The analytical results show that the anharmonic correlated Einstein model is suitable for analyzing the experimental XAFS data of metals.

Unraveling the Catalytic Mechanism of β-Cyclodextrin in the Vitamin D Formation.

Previous experimental studies have shown that the isomerization reaction of previtamin D3 (PreD3) to vitamin D3 (VitD3) is accelerated 40-fold when it takes place within a β-cyclodextrin dimer, in comparison to the reaction occurring in conventional isotropic solutions. In this study, we employ quantum mechanics-based molecular dynamics (MD) simulations and statistical multistructural variational transition state theory to unveil the origin of this acceleration. We find that the conformational landscape in the PreD3 isomerization is highly dependent on whether the system is encapsulated. In isotropic media, the triene moiety of the PreD3 exhibits a rich torsional flexibility. However, when encapsulated, such a flexibility is limited to a more confined conformational space. In both scenarios, our calculated rate constants are in close agreement with experimental results and allow us to identify the PreD3 flexibility restriction as the primary catalytic factor. These findings enhance our understanding of VitD3 isomerization and underscore the significance of MD and environmental factors in biochemical modeling.

A method for predicting the entropy and Gibbs free energy of ICl and BrCl gases based on an improved Hulburt-Hirschfelder potential

Abstract Combined with the Rydberg-Klein-Rees (RKR) data and spectral constants, a method based an improved Hulburt-Hirschfelder (IHH) potential model for calculating the molar entropy and Gibbs free energy of diatomic gases is presented. The full set of rovibrational energy is calculated by solving the one-dimension Schrödinger equation using the determined IHH potential pointwise data, and then the partition function, Gibbs free energy and entropy of the diatomic molecular gas can be determined using the quantum statistical ensemble theory. Comparing with other potentials and thermodynamic data, the application to the ground electronic state of ICl and BrCl gases shows that the IHH potential fits well with the experimental RKR data, and the calculated Gibbs free energy and molar entropy are in good agreement with the experimental values.

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.

Quantum field corrections of the equation of state in cosmological space-time

A proper quantum statistical field theory framework for the decoupling of the cosmological plasma in curved space-time implies the appearance of corrections to the classical kinetic form of the stress-energy tensor of freely streaming particles. Such quantum corrections can become relevant even at long times after the decoupling and can significantly modify the relation between energy density and pressure, that is the equation of state.

The temperature dependence on the coherence time of a quantum pseudodot qubit

In this work, the energies and eigenfunctions of ground state and first-excited states (GFES) of a strongly coupled polaron in a quantum pseudo-dot (QPD) were studied by using variational method of Pekar type (VMPT). A single qubit can be realized in this two-level quantum system. Then, we calculated the coherence time of a QPD qubit by employing the Fermi Golden Rule. The temperature effects on the coherence time are taken into account by using the quantum statistics theory (QST) and self-consistent calculation method. According to the obtained results, it is found that the coherence time increases with decreasing temperature. Also, this time is a decaying function of the chemical potential of the two-dimensional electron gas and the zero point of the PHP.

Theoretical study on macroscopic thermodynamic properties of NO<sup>+</sup> ion system

<sec>NO<sup>+</sup> is one of the most important ions in the atmospheric ionosphere and ionospheric phenomena such as auroras, and is one of the most stable diatomic cations existing in interstellar clouds. It is crucial to understand the thermodynamic properties of NO<sup>+</sup> ion for exploring the composition of interstellar gas. To obtain macroscopic thermodynamic properties of diatomic molecules and ions, a practical theoretical method is to determine the partition function associated with a potential model. This approach can be used to calculate various thermodynamic properties of the system based on the microscopic information.</sec><sec>In this work, the improved Hulbert-Hirschfelder (IHH) based potential energy model is used to simulate the potential energy curve of NO<sup>+</sup> in the ground electronic state. Then, the rovibrational energy levels for the ground electronic state of the NO<sup>+</sup> are obtained by numerically solving the radial Schrödinger equation through using the LEVEL program for the IHH potential function. Finally, the total partition function and the thermodynamic properties such as the molar heat capacity, entropy, enthalpy and reduced molar Gibbs free energy of NO<sup>+</sup> in a temperature range of 100–6000 K are calculated in the frame of the quantum statistical ensemble theory. The comparison indicates that the potential energy curve calculated based on IHH potential energy function is in better agreement with the experimental data. The root mean square error of IHH potential and experimental Rydberg-Klein-Rees (RKR) potential is 96.9 cm<sup>–1</sup>, the root mean square error of Hulbert-Hirschfelder (HH) potential is 112.7 cm<sup>–1</sup>, and the root mean square error of MRCI/aug-cc-pV6Z potential is 133 cm<sup>–1</sup>. And the macroscopic thermodynamic properties of NO<sup>+</sup> predicted by IHH are closer to the experimental values, which shows that the IHH potential model is also applicable to the ion system.</sec><sec>A feasible method is presented to obtain the thermodynamic properties of gaseous diatomic ions based on microscopic information by constructing reliable analytical potential energy function associated with quantum statistical ensemble theory.</sec>

Quantum statistical theory for an exciton-polariton condensate: Fluctuations and coherence

A full quantum theory beyond the mean-field regime is developed for an exciton-polariton condensate, for a complete understanding of quantum fluctuations. We find an analytical solution for the polariton density matrix, showing the nonlinearity causing fast relaxation correlated with the pump so as to yield the quantum condensation above threshold. Increasing the pump intensity, a nonequilibrium phase transition towards the condensation of the lower polaritons emerges, with a statistics transiting from a thermal, through a super-Poissonian, and towards a nonclassical distribution; the latter two possess off-diagonal long-range order but the last one is beyond. The results signify the role of dark states for polariton fluctuations, and lead to a nonclassical counting statistics of emitted photons, which elaborates the role of the key parameters, e.g., pump, detuning, and temperature.

Asymmetrical Gaussian Potential Effects on Strongly Coupled Magnetopolaron Properties in Triangular Confinement Potential Quantum Wells

In this research, the existence of an asymmetrical Gaussian confinement potential (AGCP) along the quantum well (QW) growth direction and of a parabolic potential perpendicular to the polar coordinate direction were considered. The magnetic field and temperature properties of the longitudinal optical (LO)-phonon mean number, ground-state energy (GSE), ground-state binding energy (GSBE) and vibrational frequency (VF) of strongly coupled magnetopolarons in triangular confinement potential QWs (TCPQWs) were investigated according to the quantum statistical theory as well as the linear combination operator and unitary transformation methods. We obtained analytical expressions for the GSE, GSBE, VF and LO-phonon mean number as functions of the applied magnetic field, temperature, AGCP barrier height, AGCP range, polar coordinate system’s polar angle and polar coordinate system’s confinement strength. It was demonstrated by the calculated numerical results that the GSE, GSBE, VF and LO-phonon mean number varied with the related physical quantities. The obtained theoretical results are expected to provide a reference for future research on polarons.

Study on macroscopic thermodynamic properties of ClO molecule based on the improved Hulburt–Hirschfelder potential energy function

AbstractThe improved Hulburt–Hirschfelder potential energy function is used as a proposal to emulate the behavior of intramolecular motion of a gas composed of diatomic molecules. In this work, the rovibrational energies of ClO molecule in the ground electronic state are obtained by solving the one‐dimensional Schrödinger equation with the improved Hulburt–Hirschfelder potential energy curve. And then, the molar heat capacities, molar entropies, molar enthalpies and reduced Gibbs free energies of ClO macroscopic gas are calculated by the quantum statistical ensemble theory. The results are compared with those calculated by using RKR potential energy curve from experiment and Morse potential energy function. It is found that the macroscopic thermodynamic properties of ClO calculated by the improved Hulburt–Hirschfelder potential energy function are closer to the experimental values, which provides a new way to calculate the macroscopic thermodynamic quantities of diatomic gas based on molecular microscopic information.

Temperature dependence on transition frequency and energy-levels of longitudinal-acoustic polaron in monolayer graphene under an external field

The longitudinal-acoustic (LA) polaron properties in monolayer graphene under an external magnetic field were investigated using Lee-Low-Pines unitary transformation and a linear combination operator. The effects of temperature on the ground state and first excited state (FES) energy, transition frequency, and the mean number of LA phonons were then examined using quantum statistics theory. The results revealed the emergence of a like-bandgap by splitting the energy levels and transition frequency. The like-bandgap was also dependent on the Debye cut-off, magnetic field strength, and temperature, whereas the mean number of LA phonons was increased by magnetic field strength and temperature. Finally, the results demonstrated that changing the system temperature, Debye cut-off wavenumber, and magnetic field strength could control the energy levels, transition frequency, like-bandgap, and several LA phonons.

Physics of PT -symmetric quantum systems at finite temperatures

We study parity-time-symmetric non-Hermitian quantum systems at finite temperature, where the Boltzmann distribution law fails to hold. To characterize their abnormal physical properties, a new quantum statistics theory (the so-called quantum Liouvillian statistics theory) was developed, in which the Boltzmann distribution law was replaced by the Liouvillian-Boltzmann distribution law. Using it, we derived analytical results of thermodynamic properties for thermal PT systems and found that a "continuous" thermodynamic phase transition occurs at the exceptional point, where a zero-temperature anomaly exists.

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson–Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1≤c≤0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration cp. The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

Temperature effect of strong-coupling polaron in RbCl quantum wells with double asymmetric confined potentials

In this study, the ground state properties of strong-coupling polaron in RbCl quantum wells (QWs) by using double asymmetric confined potential were theoretically investigated based on effective mass approximation. Ground state binding energy (GSBE), ground state energy (GSE), vibrational frequency (VF), and mean LO phonon number (MLOPN) were obtained as functions of asymmetric confinement potential parameters in QWs by using the unitary transformation method and linear combination operator. GSBE, GSE, VF and MLOPN were found to be increasing functions of asymmetric semi-exponential confinement potential (ASECP) parameter [Formula: see text] and decreasing functions of parameter [Formula: see text]. GSE was rapidly increased with the increase of confinement strength. GSBE, GSE, VF and MLOPN increase as the increasing (decreasing) of anisotropic parabolic confinement potential strength (confinement length). In addition, the temperature effect was evaluated by using quantum statistical theory. With the increase of temperature, GSE and GSBE decreased while VF and MNLOP increased.

Constraining Non-Dissipative Transport Coefficients in Global Equilibrium

The fluid in global equilibrium must fulfill some constraints. These constraints can be derived from quantum statistical theory or kinetic theory. In this work, we show how these constraints can be applied to determine the non-dissipative transport coefficients for chiral systems along with the energy-momentum conservation, chiral anomaly for charge current and trace anomaly in the energy-momentum tensor.

Thermal expansion of FeNi Invar and zinc-blende CdTe from the view point of local structure

Thermal expansion of FeNi Invar and zinc-blende CdTe was investigated from the view point of local structure using the extended x-ray absorption fine structure (EXAFS) spectroscopic data and the path-integral effective classical potential (PIECP) Monte Carlo computational simulations. In this Review article, first the quantum statistical perturbation theory is intuitively described to see different character concerning thermal expansion between the quantum and classical theories. The diatomic Br2 molecule is employed as a simple example. Second, the PIECP theory is briefly described to note advantages and disadvantages of this simulation technique. Historical background is also discussed for the EXAFS investigation of thermal expansion based on the quantum statistical theories. The results of the FeNi Invar alloy are then summarized. The origin of zero thermal expansion in the FeNi alloy is ascribed to the so-called Invar effect that implies the variation of the electronic structure of Fe atoms depending on temperature. Zero thermal expansion at low temperature is however found to originate from the vibrational quantum effect. It is also noted that the interatomic distances of Fe-Fe, Fe-Ni, and Ni-Ni pairs are slightly but meaningfully different from each other, although the alloy exhibit a simple fcc crystal. Such a pair- dependent difference is also true for thermal expansion and we will discuss thermal expansion from the local point of view, which is interestingly different from the lattice thermal expansion significantly. Finally, the results of the zinc blende (or diamond) structure are presented. Although the origin of negative thermal expansion in these tetrahedral crystals is known as a result of classical vibrational anomaly within the Newton dynamics theory, the quantum statistical simulation is found to be essential to reproduce the negative thermal expansion of CdTe. It is emphasized that the vibrational quantum effect and classical anharmonicity are of great importance for the understanding of low-temperature thermal expansion as well as the elastic constants.

Semi-infinite metallic system: QST versus DFT

Modeling and investigation of thermodynamic characteristics of spatially-finite metallic systems is an essential task of modern nanophysics. We show that the widely used DFT (density functional theory) is less efficient than the QST (quantum-statistical theory) approach.

Calculating macroscopic gas molar heat capacity of SO molecule based on rovibrational energy level

<sec>Sulfur oxide (SO) is a kind of well-known diatomic molecule which becomes one of the major pollutants in the atmosphere. Control of the heat capacity of SO molecule is of great significance for elucidating its macroscopic evolution process. In the research of macroscopic systems composed of many particles as well as several matters, it is an important approach to obtain macroscopic thermodynamic quantities of the system by constructing a partition function from the microscopic information of molecule. For diatomic molecules in a certain electronic state, the partition function can directly be obtained by calculating the rovibrational energy of the system to acquire the macroscopic molar heat capacities.</sec><sec>In this work, the contribution of rotational behavior to molar heat capacity is further considered. The potential energy function for the ground electronic state of SO is constructed by the variational algebraic method (VAM) and RKR (Rydberg-Klein-Rees) method, in which the former one can determine the complete vibrational energy levels of an electronic state of a molecule. The rovibrational energy level of the system is obtained by analytical solution, and then the molar heat capacity of SO macroscopic gas in the temperature range of 300–6000 K is calculated by quantum statistical ensemble theory The above calculation depends only on the experimental vibrational energy, experimental rotational spectral constant and the dissociation energy of SO molecule. Fortunately, through comparison between theoretical calculation results and experimental data, we find that the molar heat capacity of gaseous SO molecule can be well predicted by employing the full set of rovibrational energy to describe the internal vibration and rotation of SO molecule. The idea of calculating the molar heat capacity by using the full set of rovibrational energy makes up for the shortcomings of previous work where molar heat capacity is calculated by using the approximate model characterizing the molecular rotational behavior, and also provides a new research paradigm for solving macro thermodynamic quantities based on micro statistical processes .</sec>

Improved computational modeling of the kinetics of the acetylperoxy + HO2 reaction.

The acetylperoxy + HO2 reaction has multiple impacts on the troposphere, with a triplet pathway leading to peracetic acid + O2 (reaction (1a)) competing with singlet pathways leading to acetic acid + O3 (reaction (1b)) and acetoxy + OH + O2 (reaction (1c)). A recent experimental study has reported branching fractions for these three pathways (α1a, α1b, and α1c) from 229 K to 294 K. We constructed a theoretical model for predicting α1a, α1b, and α1c using quantum chemical and Rice-Ramsperger-Kassel-Marcus/master equation (RRKM/ME) simulations. Our main quantum chemical method was Weizmann-1 Brueckner Doubles (W1BD) theory; we combined W1BD and equation-of-motion spin-flip coupled cluster (SF) theory to treat open-shell singlet structures. Using RRKM/ME simulations that included all conformers of acetylperoxy-HO2 pre-reactive complexes led to a 298 K triplet rate constant, k1a = 5.11 × 10-12 cm3 per molecule per s, and values of α1a in excellent agreement with experiment. Increasing the energies of all singlet structures by 0.9 kcal mol-1 led to a combined singlet rate constant, k1b+1c = 1.20 × 10-11 cm3 per molecule per s, in good agreement with experiment. However, our predicted variations in α1b and α1c with temperature are not nearly as large as those measured, perhaps due to the inadequacy of SF theory in treating the transition structures controlling acetic acid + O3 formation vs. acetoxy + OH + O2 formation.