Thermodynamics of fermions at any temperature based on parametrized partition function.

In this work, we study the recently developed parametrized partition function formulation and show how we can infer the thermodynamic properties of fermions based on numerical simulation of bosons and distinguishable particles at various temperatures. In particular, we show that in the three-dimensional space defined by energy, temperature, and the parameter characterizing parametrized partition function, we can map the energies of bosons and distinguishable particles to fermionic energies through constant-energy contours. We apply this idea to both noninteracting and interacting Fermi systems and show it is possible to infer the fermionic energies at all temperatures, thus providing a practical and efficient approach to obtain thermodynamic properties of Fermi systems with numerical simulation. As an example, we present energies and heat capacities for 10 noninteracting fermions and 10 interacting fermions and show good agreement with the analytical result for the noninteracting case.

Path-integral molecular dynamics for anyons, bosons, and fermions.

In this article we develop a general method to numerically calculate physical properties for a system of anyons with path integral molecular dynamics. We provide a unified method to calculate the thermodynamics of identical bosons, fermions, and anyons. Our method is tested and applied to systems of anyons, bosons, and fermions in a two-dimensional harmonic trap. We also consider a method to calculate the energy for fermions as an application of the path integral molecular dynamics to simulate the anyon model.

On the thermodynamic properties of fictitious identical particles and the application to fermion sign problem.

By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter ξ interpolating continuously between bosons (ξ = 1) and fermions (ξ = -1). Through general analysis and numerical experiments, we find that the average energy may have good analytical properties as a function of this real parameter ξ, which provides the chance to calculate the thermodynamical properties of identical fermions by extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for ξ ≥ 0. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion sign problem for some quantum systems.

Path integral molecular dynamics for thermodynamics and Green's function of ultracold spinor bosons.

Most recently, the path integral molecular dynamics has been successfully used to consider the thermodynamics of single-component identical bosons and fermions. In this work, the path integral molecular dynamics is developed to simulate thermodynamics, Green's function, and momentum distribution of two-component bosons in three dimensions. As an example of our general method, we consider the thermodynamics of up to 16 bosons in a three-dimensional harmonic trap. For noninteracting spinor bosons, our simulation shows a bump in the heat capacity. As the repulsive interaction strength increases, however, we find the gradual disappearance of the bump in the heat capacity. We believe that this simulation result can be tested by ultracold spinor bosons with optical lattices and magnetic-field Feshbach resonance to tune the inter-particle interaction. We also calculate Green's function and momentum distribution of spinor bosons. Our work facilitates the exact numerical simulation of spinor bosons, whose property is one of the major problems in ultracold Bose gases.

Numerical calculation of Green's function and momentum distribution for spin-polarized fermions by path integral molecular dynamics.

Most recently, path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of identical bosons and fermions by Hirshberg et al. In this work, we demonstrate that PIMD can be developed to calculate Green's function and extract momentum distributions for spin-polarized fermions. In particular, we show that the momentum distribution calculated by PIMD has potential applications to numerous quantum systems, e.g., ultracold fermionic atoms in optical lattices.

Path integral molecular dynamics simulations for Green's function in a system of identical bosons.

Path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of large bosonic systems in a recent study [Hirshberg et al., Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)]. In this work, we extend PIMD techniques to study Green's function for bosonic systems. We demonstrate that the development of the original PIMD method enables us to calculate Green's function and extract momentum distribution from our simulations. We also apply our method to systems of identical interacting bosons to study Berezinskii-Kosterlitz-Thouless transition around its critical temperature.

On the Thermodynamic Origin of Gravitational Force by Applying Spacetime Entanglement Entropy and the Unruh Effect.

We consider the thermodynamic origin of the gravitational force of matter by applying the spacetime entanglement entropy and the Unruh effect originating from vacuum quantum fluctuations. By analyzing both the local thermal equilibrium and quasi-static processes of a system, we may get both the magnitude and direction of Newton's gravitational force in our theoretical model. Our work shows the possibility that the elusive Unruh effect has already shown its manifestation through gravitational force.

An eight-dimensional quantum mechanical Hamiltonian for X + YCZ3 system and its applications to H + CH4 reaction.

An eight-dimensional quantum mechanical Hamiltonian has been proposed based on Palma and Clary's model in which the non-reacting CZ(3) group keeps a C(3v) symmetry in the X + YCZ(3) ↔ XY + CZ(3) reaction J. Palma and D. C. Clary [J. Chem. Phys. 112, 1859 (2000)]. By transforming the original cartesian coordinate system (x, s) into a scaled polar coordinate system (q, γ), the vibrational Hamiltonian of CZ(3) group is expressed in a simple form with a clear physical picture. This Hamiltonian is used to investigate the H + CH(4) → H(2) + CH(3) reaction on the Jordan-Gilbert potential energy surface. The total reaction probabilities are calculated for the initial ground state, and umbrella, bending, symmetric, and asymmetric stretching excited states of CH(4) with total angular momentum J = 0. The integral cross sections for the reaction are also studied for these initial vibrational states with a centrifugal-sudden approximation. The total integral cross sections for the asymmetric stretching vibrational excited state are in good agreement with the experimental observations. The results also showed the difference of dynamical behavior between reactions from symmetric and asymmetric stretching excited states. The thermal rate constants are calculated for the temperature range T = 250-2000 K and compared with the experimental and other theoretical results.

Ultracold two-component fermionic gases with a magnetic field gradient near a feshbach resonance.

We study theoretically the ultracold two-component fermionic gases when a gradient magnetic field is used to tune the scattering length between atoms. For 6Li at the narrow resonance B0=543.25 G, it is shown that the gases would be in a coexistence of the regimes of BCS, Bose-Einstein condensation (BEC), and unitarity limit with the present experimental technique. In the case of thermal and chemical equilibrium, we investigate the density distribution of the gases and show that a double peak of the density distribution can give us a clear evidence for the coexistence of BCS, BEC, and unitarity limit.