The ideal Boson gas in an external scalar potential

We consider a new way of going to the infinite volume thermodynamic limit for a finite density quantum system and apply it to the case of an ideal Boson gas. We describe two procedures for calculating the particle density in the thermodynamic limit, one local and one global, and show that they give different values for the density. Further calculations show that this discrepancy is caused by lack of macroscopic translation invariance of the system, which is not apparent at the microscopic level. We calculate the limiting value of the expectation function of the Weyl operators both above and below the critical density for Bose-Einstein condensation, and show that the condensate has paradoxical properties of a similar type to those recently discovered for the rotating Boson gas.     

Equation of state of an interacting bose gas confined by a harmonic trap: the role of the "harmonic" pressure

A gas of interacting atoms confined by a three dimensional anisotropic harmonic potential is studied. It is shown that there appear "new" thermodynamic variables instead of the usual pressure and volume: the latter is replaced by (the inverse of) the cube of the geometric average of the oscillator frequencies of the trap, and the former by the harmonic pressure responsible for the mechanical equilibrium of the fluid in the trap. We discuss the origin and physical meaning of these quantities and show that the equation of state of the gas is given in terms of these variables. The equation of state of a cold gas of interacting Bose atoms in the Hartree-Fock approximation is presented. We indicate how the harmonic pressure can be measured in current experiments.     

Transition temperatures of the trapped ideal spinor Bose gas

The thermodynamic properties of the trapped ideal spinor Bose gas are studied in details with the constraints of fixed total number of atoms N, and magnetization M. The double transition temperatures, their corresponding corrections due to finite particle number, and the population of each component are investigated. The generalization to the ideal spinor Bose gas of hyperfine quantum number F is also discussed. We propose that the order and disorder parameters to describe the symmetry broken of condensation.     

The large deviation principle and some models of an interacting boson gas

This is a study of the equilibrium thermodynamics of the Huang-Yang-Luttinger model of a boson gas with a hard-sphere repulsion using large deviation methods; we contrast its properties with those of the mean field model. We prove the existence of the grand canonical pressure in the thermodynamic limit and derive two alternative expressions for the pressure as a function of the chemical potential. We prove the existence of condensate for values of the chemical potential above a critical value and verify a prediction of Thouless that there is a jump in the density of condensate at the critical value. We show also that, at fixed mean density, the density of condensate is an increasing function of the strength of the repulsive interaction. In an appendix, we give proofs of the large deviation results used in the body of the paper.     

Numerical procedures for natural gas accurate thermodynamic properties calculation

Natural gas (NG) is a mixture of 21 elements and widely used in the industries and domestics. Knowledge of its thermodynamic properties is essential for designing appropriate process and equipments. In this study, the detailed numerical procedures for computing most thermodynamic properties of natural gas are discussed based on the AGA8 equation of state (EOS) and thermodynamics relationships. To validate the procedures, the numerical values are compared with available measured values. The validations show that the average absolute percent deviation (AAPD) for density calculations is 0.0831%, for heat capacity at the constant pressure is 0.87%, for heat capacity at the constant volume is 1.13%, for Joule-Thomson coefficient is 1.93%, for speed of sound is 0.133%, and for enthalpy is 1.06%. Furthermore, in this work, the new procedures are presented for computing the entropy and internal energy. Due to lack of experimental data for these properties, the validation is done for pure methane. The validation shows that AAPD is 0.078% and 0.0133% for internal energy and entropy, respectively.     

Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle

Applying finite time thermodynamics theory and the non-dominated sorting genetic algorithm-II (NSGA-II), thermodynamic analysis and multi-objective optimization of an irreversible Diesel cycle are performed. Through numerical calculations, the impact of the cycle temperature ratio on the power density of the cycle is analyzed. The characteristic relationships among the cycle power density versus the compression ratio and thermal efficiency are obtained with three different loss issues. The thermal efficiency, the maximum specific volume (the size of the total volume of the cylinder), and the maximum pressure ratio are compared under the maximum power output and the maximum power density criteria. Using NSGA-II, single-, bi-, tri-, and quadru-objective optimizations are performed for an irreversible Diesel cycle by introducing dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density as objectives, respectively. The optimal design plan is obtained by using three solution methods, that is, the linear programming technique for multidimensional analysis of preference (LINMAP), the technique for order preferences by similarity to ideal solution (TOPSIS), and Shannon entropy, to compare the results under different objective function combinations. The comparison results indicate that the deviation index of multi-objective optimization is small. When taking the dimensionless power output, dimensionless ecological function, and dimensionless power density as the objective function to perform tri-objective optimization, the LINMAP solution is used to obtain the minimum deviation index. The deviation index at this time is 0.1333, and the design scheme is closer to the ideal scheme.     

Dynamical role of anyonic excitation statistics in rapidly rotating bose gases

We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a dynamical role. For particular values of the two-dimensional coupling constant g=-2pih2(2k-1)/m, where k is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.     

Planck's experiment on gas mixing,Gibbs' paradox and the definition of entropy in statistical mechanics

The interpretation of entropy provided by statistical thermodynamics is not adequate to represent the thermodynamic entropy of the gas of noninteracting particles considered in this theory. Planck's thought experiment on reversible mixing and Gibbs' paradox provide perhaps the best-known evidence of this. The assumption that the internal energy of an ideal gas depends only on its temperature is introduced both in the kinetic theory of gases and in the classical thermodynamics. Such an assumption is no doubt adequate to deal with real gases at appropriately low pressures and high temperatures. However, the present paper shows that the same assumption implies that the entropy of an ideal gas, like its internal energy, must also depend only on temperature. The paper calculates the expression of the entropy function that is consistent with the internal energy function of the gas. From this expression, the thermodynamic entropy of the ideal gas – as distinct from its statistical entropy – is finally expressed in terms of statistical mechanics variables.     

Critical point of an interacting two-dimensional atomic Bose gas

We have measured the critical atom number in an array of harmonically trapped two-dimensional (2D) Bose gases of rubidium atoms at different temperatures. We found this number to be about 5 times higher than predicted by the semiclassical theory of Bose-Einstein condensation (BEC) in the ideal gas. This demonstrates that the conventional BEC picture is inapplicable in an interacting 2D atomic gas, in sharp contrast to the three-dimensional case. A simple heuristic model based on the Berezinskii-Kosterlitz-Thouless theory of 2D superfluidity and the local density approximation accounts well for our experimental results.     

Thermodynamic properties of a finite Bose gas in a harmonic trap

We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.     

Wavy fronts in reaction-diffusion systems with cross advection

Using a field-theoretic approach, we systematically generalize the usual semiclassical approximation for a harmonically trapped ideal Bose gas in such a way that its range of applicability is essentially extended. With this we can analytically calculate thermodynamic properties even for small particle numbers. In particular, it now becomes possible to determine the critical temperature as well as the temperature dependence of both heat capacity and condensate fraction in low-dimensional traps, where the standard semiclassical approximation is not even applicable.     

Exploring the thermodynamics of a two-dimensional Bose gas

Using in situ measurements on a quasi-two-dimensional, harmonically trapped (87)Rb gas, we infer various equations of state for the equivalent homogeneous fluid. From the dependence of the total atom number and the central density of our clouds with chemical potential and temperature, we obtain the equations of state for the pressure and the phase-space density. Then, using the approximate scale invariance of this 2D system, we determine the entropy per particle and find very low values (below 0.1k(B)) in the strongly degenerate regime. This shows that this gas can constitute an efficient coolant for other quantum fluids. We also explain how to disentangle the various contributions (kinetic, potential, interaction) to the energy of the trapped gas using a time-of-flight method, from which we infer the reduction of density fluctuations in a nonfully coherent cloud.     

Bose–Einstein condensation versus Dicke–Hepp–Lieb transition in an optical cavity

We provide an exact solution for the interplay between Bose–Einstein condensation and the Dicke–Hepp–Lieb self-organization transition of an ideal Bose gas trapped inside a single-mode optical cavity and subject to a transverse laser drive. Based on an effective action approach, we determine the full phase diagram at arbitrary temperature, which features a bi-critical point where the transitions cross. We calculate the dynamically generated band structure of the atoms and the associated suppression of the critical temperature for Bose–Einstein condensation in the phase with a spontaneous periodic density modulation. Moreover, we determine the evolution of the polariton spectrum due to the coupling of the cavity photons and the atomic field near the self-organization transition, which is quite different above or below the Bose–Einstein condensation temperature. At low temperatures, the critical value of the Dicke–Hepp–Lieb transition decreases with temperature and thus thermal fluctuations can enhance the tendency to a periodic arrangement of the atoms.     

Study for particular solutions of cylindrical shock waves in magnetogasdynamics

In this research article, a problem of shock waves propagation in magnetogasdynamics is considered in ideal gas. The problem can be represented by hyperbolic non-linear system of partial differential equations (PDEs). It is solved by similarity method under invariant surface conditions. I reduced non-linear system of magnetogasdynamics into first order system of ordinary differential equations (ODEs) and it is non-linear. The ratio of heat capacity at constant pressure to heat capacity at constant volume is also known as the adiabatic constant and their values for monatomic, diatomic gasses are more than one in ideal gas. So, I have obtained exact solution of magnetogasdynamics system in ideal gas for particular value of adiabatic index$\gamma =2$. The effect of the ambient density exponent $\theta$ on flow quantities density, velocity, pressure, and magnetic field are determined before the shock.     

Molecular dynamics study of Laplace pressure in solid-state nanostructures

The paper provides a comprehensive molecular dynamics study of nanostructures compressed by a system of surface atoms to analyze their surface tension. Surface tension is here understood as phenomena resulting from the presence of surface atoms. All main properties of nanostructures are conditioned by a highly developed surface. The number of surface atoms and their energy are comparable to those of bulk atoms.It is shown that at cryogenic temperatures, spherical solid-state clusters of size up to 10 nm reveal excess pressure. This pressure owes to compression of the clusters by surface atoms.The molecular dynamics study of thermodynamic properties of the nanostructures demonstrates that the increase in pressure in clusters of size from 2 to 9 nm with temperature is due to the gas component and the slope on the temperature dependence of thermal pressure does not depend on the cluster size. It is also shown that the surface tension coefficient decreases with an increase in temperature. A theoretical expression for this dependence is derived suggesting that there exists a certain Laplace temperature at which compressive pressure in a cluster is balanced by thermal gas pressure.     

Exact pairing correlations for one-dimensionally trapped fermions with stochastic mean-field wave functions

The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudopotential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For a harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For a few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated.     

原子激射器的空间有效增益范围

求出了γ维空间中理想玻色气体的态密度,采用Thomas-Fermi近似,导出了γ维广义幂律势阱中粒子数密度的空间分布.在此基础上,求出了原子激射器的空间有效增益范围(即γ维势阱中玻色-爱因斯坦凝聚的空间有效范围),并对其产生影响的相关因素进行了讨论.     

The simple fundamental equation of state for liquid,gas, and fluid of xenon

To describe the thermodynamic properties of xenon, a new fundamental low-parametric equation of state (in the form of reduced Helmholtz energy) is obtained with the help of the methods and approaches developed by the authors. It allows us to describe the thermal properties of gas, liquid, and fluid with a sufficiently high accuracy close to the accuracy of experiment in a range from the density in the ideal gas state to the density at the triple point, excluding the critical region. The caloric properties and speed of xenon sound are calculated without involving any caloric data, with the exception of ideal gas enthalpy. The values of isobaric heat capacity, sound speed, and other thermodynamic properties obtained by calculations are in good agreement with the experimental data.     

High temperature BEC with photon-like atomic polaritons

We consider the problem of high temperature (room and beyond) true Bose-Einstein condensation (BEC) of trapped ideal 1D gas of low branch (LB) atomic polaritons for the system of two-level atomic ensemble interacting with a quantized single-mode electromagnetic field in the presence of optical collisions (OC) with buffer gas atoms. We discuss the application of biconical waveguide cavity (BWC) for observing predicted effects.     

Derivation of the Onsager principle from large deviation theory

The Onsager linear relations between macroscopic flows and thermodynamics forces are derived from the point of view of large deviation theory. For a given set of macroscopic variables, we consider the short-time evolution of near-equilibrium fluctuations, represented as the limit of finite-size conditional expectations. The resulting asymptotic conditional expectation is taken to represent the typical macrostate of the system and is used in place of the usual time-averaged macrostate of traditional approaches. By expanding in the short-time, near-equilibrium limit and equating the large deviation rate function with the thermodynamic entropy, a linear relation is obtained between the time rate of change of the macrostate and the conjugate initial macrostate. A Green–Kubo formula for the Onsager matrix is derived and shown to be positive semi-definite, while the Onsager reciprocity relations readily follow from time reversal invariance. Although the initial tendency of a macroscopic variable is to evolve towards equilibrium, we find that this evolution need not be monotonic. The example of an ideal Knundsen gas is considered as an illustration.