The recently proposed macroscopic quantum phenomenon, Temperature-Induced Quantum Migration (TIQM), causes local heating and cooling and significantly affects the local heat capacity of a noninteracting confined Maxwell-Boltzmann gas. TIQM guarantees the non-negativity of local heat capacity at low temperatures, results in a substantial local heat-capacity overshoot, and provides a physical basis for global heat-capacity maxima and thermal confinement energy. We extend this framework here to Bose gases in three different rectangular domains, effectively providing three-dimensional (3D)/two-dimensional (2D)/one-dimensional (1D) confinement at high temperatures while transitioning to 2D/1D/zero-dimensional (0D) at low temperatures, thus inducing dimensional crossovers during temperature changes. We demonstrate that quantum degeneracy enhances the TIQM process, resulting in dimension-dependent effects on local and global heat capacities. For the 3D-2D crossover, TIQM leads to a giant excess local heat capacity and explains the mechanism for the enhancement of the global heat-capacity maximum, which surpasses the unconfined ideal Bose gas limit (1.93), reaching 1.97 at a finite density. Conversely, for the 2D-1D and 1D-0D crossovers, the excess local heat capacity diminishes with increasing quantum degeneracy (density), while it is TIQM alone that becomes responsible for excess global heat capacity. For the 1D-0D crossover, we find that only single-particle ergodic systems can have a global excess heat capacity; otherwise, the maximum behavior disappears completely. TIQM also provides a mechanism for the thermal confinement energy in Bose gases.
The recently proposed macroscopic quantum phenomenon, Temperature-Induced Quantum Migration (TIQM), causes local heating and cooling and significantly affects the local heat capacity of a noninteracting confined Maxwell-Boltzmann gas. TIQM guarantees the non-negativity of local heat capacity at low temperatures, results in a substantial local heat-capacity overshoot, and provides a physical basis for global heat-capacity maxima and thermal confinement energy. We extend this framework here to Bose gases in three different rectangular domains, effectively providing three-dimensional (3D)/two-dimensional (2D)/one-dimensional (1D) confinement at high temperatures while transitioning to 2D/1D/zero-dimensional (0D) at low temperatures, thus inducing dimensional crossovers during temperature changes. We demonstrate that quantum degeneracy enhances the TIQM process, resulting in dimension-dependent effects on local and global heat capacities. For the 3D-2D crossover, TIQM leads to a giant excess local heat capacity and explains the mechanism for the enhancement of the global heat-capacity maximum, which surpasses the unconfined ideal Bose gas limit (1.93), reaching 1.97 at a finite density. Conversely, for the 2D-1D and 1D-0D crossovers, the excess local heat capacity diminishes with increasing quantum degeneracy (density), while it is TIQM alone that becomes responsible for excess global heat capacity. For the 1D-0D crossover, we find that only single-particle ergodic systems can have a global excess heat capacity; otherwise, the maximum behavior disappears completely. TIQM also provides a mechanism for the thermal confinement energy in Bose gases.
Temperature-Induced Quantum Migration (TIQM) is a macroscopic quantum phenomenon that fundamentally reshapes the local thermodynamics of confined systems. While previously explored in Maxwell-Boltzmann and Bose gases, we here extend the TIQM framework to noninteracting Fermi gases confined in anisometric rectangular domains. These domains are characterized by D_{I}, representing the number of dimensions that remain unconfined. We derive the local heat capacity and demonstrate that the standard temperature derivative of local energy yields unphysical negative regions, a discrepancy resolved by the TIQM correction. We show that quantum degeneracy in Fermi gases generally suppresses the TIQM contribution to global heat capacity compared to other statistics, yet it drives a distinct redistribution of local heat capacity. Notably, for the most constrained case (D_{I}=0), a Schottky-type anomaly emerges at low densities, which is progressively "washed out" by increasing dimensionality (D_{I}=1,2). Based on an idealized noninteracting model, our calculations suggest that a measurable (22%) enhancement in the local-to-global electronic heat capacity ratio could emerge at approximately 84 nm from the longitudinal boundaries of a 12×12×5600 nm^{3} bismuth nanowire at 30 K, offering a potential experimental signature for TIQM. These results complete a systematic trilogy of studies across all fundamental quantum statistics, establishing TIQM as a necessary correction for the local thermodynamics of nanoscale devices.
We obtain the thermodynamic properties for a noninteracting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P\ensuremath{\geqslant}0$ between layers. The BEC critical temperature Tc coincides with the ideal gas BEC critical temperature T0 when P=0 and rapidly goes to zero as P increases to infinity for any finite interlayer separation. The specific heat CV as a function of absolute temperature T for finite P and plane separation a exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than that of BEC Tc. This highlights the effects due to particle confinement. We then discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of P. For T<Tc the crossover is revealed by a change in slope of logCV(T) and when T>Tc, it is exhibited by a broad minimum in CV(T).
In this paper, we calculate the equations of state and the thermodynamic quantities for two- and three-dimensional hard-sphere Bose and Fermi gases in finite-size containers. The approach we used to deal with interacting gases is to convert the effect of interparticle hard-sphere interaction to a kind of boundary effect, and then the problem of a confined hard-sphere quantum gas is converted to the problem of a confined ideal quantum gas with a complex boundary. For this purpose, we first develop an approach for calculating the boundary effect on d-dimensional ideal quantum gases and then calculate the equation of state for confined quantum hard-sphere gases. The thermodynamic quantities and their low-temperature and high-density expansions are also given. In higher-order contributions, there are cross terms involving both the influences of the boundary and of the interparticle interaction. We compare the effect of the boundary and the effect of the interparticle interaction. Our result shows that, at low temperatures and high densities, the ratios of the effect of the boundary to the effect of the interparticle interaction in two dimensions are essentially different to those in three dimensions: in two dimensions, the ratios for Bose systems and for Fermi systems are the same and are independent of temperatures, while in three dimensions, the ratio for Bose systems depends on temperatures, but the ratio for Fermi systems is independent of temperatures. Moreover, for three-dimensional Fermi cases, compared with the contributions from the boundary, the contributions from the interparticle interaction to entropies and specific heats are negligible.
In the one-dimensional (1D) nanopores of FSM-16 (2.8 nm in diameter) and the 3D pores of HMM-2 (2.7 nm, and 5.5 nm in 3D period), the 4 He films adsorbed on these nanopore walls show the properties of the Bose quantum fluid and superfluidity above 1.4 atomic layers at low temperatures. The boundary of the Bose fluid region was determined from the kink (peak) temperature T C of the heat capacity at each coverage n . The phase diagrams obviously show dependence on the 1D and 3D pore connections, respectively. In the 3D nanopores, the coverage (density) dependence of T C is well reproduced by the Bose-Einstein condensation temperature of the 3D ideal gas which is proportional to ( n - n c ) 2/3 , where n c is the onset coverage. In the case of the 1D pores (channels), T C is proportional to ( n - n c ) at 0.1 < T C < 1K. This T C is likely to correspond to the crossover temperature of the 2D ideal gas heat capacity from the constant heat capacity of the Boltzmann gas to the linear in T , with decreasing temperature. At T C , the thermal de Broglie wavelength of the free particle is still shorter than the pore diameter, while the thermal phonon wavelength is estimated to become longer than the diameter below T C , which indicates the 1D phonon state.
The specific heat per particle ( c v ) of an ideal gas, on many occasions, is interpreted as energy fluctuation per particle (▵ 2 ) of the ideal gas through the relation ▵ 2 = kT 2 c v , where k is the Boltzmann constant and T is the temperature. This relationship is true only in the classical limit and deviates significantly in the quantum degenerate regime. We have analytically explored quantum to classical crossover of this relationship, in particular, for 3D free Bose and Fermi gases. We have explored the same for harmonically trapped cases. We have obtained a hump of around its condensation point for 3D harmonically trapped Bose gas. We have discussed the possibility of an occurring phase transition with the discontinuity of heat capacity from the existence of such a hump for other Bose and Fermi systems.
The relationship between many-body interactions and dimensionality is integral to numerous emergent quantum phenomena.A striking example is the Bose gas, which upon confinement to one dimension (1D) obeys an infinite set of conservation laws, prohibiting thermalization and constraining dynamics.In our experiment, we demonstrate that such a 1D behavior can extend much further into the dimensional crossover toward 3D than expected.Starting from a weakly interacting Bose gas trapped in a highly elongated potential, we perform a quench to instigate the dynamics of a single density mode.Employing the theory of generalized hydrodynamics, we identify the dominant relaxation mechanism as the 1D dephasing of the relevant collective excitations of the system, the rapidities.Surprisingly, the dephasing remains dominant even for temperatures far exceeding conventional limits of one dimensionality where thermalization should occur.We attribute our observations to an emergent Pauli blocking of transverse excitations caused by the rapidities assuming fermionic statistics, despite the gas being purely bosonic.Thus, our study suggests that 1D physics is less fragile than previously thought, as it can persist even in the presence of significant perturbations.More broadly, by employing the exact Bethe ansatz solutions of the many-body system, we facilitate an interpretation of how the emergent macroscopic behavior arises from the microscopic interactions.