arXiv subjects

Q. H. Liu

Publications and source records attributed to Q. H. Liu.

At least 19 recordsLinked to original sources

arXiv2025

Singular zero-temperature system

It has long been taken for granted that there is only one type of thermodynamic system near absolute zero temperature: the ordinary one compatible with all statements of the third law, with a fundamental yet tacit assumption that all heat capacities in the system vanish as absolute temperature approaches zero. However, in the strict sense, the statements are not mutually equivalent. Once the tacit assumption is released, the inequivalence must remain, and we may have some systems that are only compatible with one or two statements but not all, defining a singular zero-temperature system which can never be excluded from physical feasibility. We revisit some previously proposed theoretical models and identify that they belong to the singular system.

cond-mat.stat-mech↗

arXiv2025

An anomalous particle-exchange mechanism for two isolated Bose gases merged into one

In an isolated ideal Bose system with a fixed energy, the number of microstates depends solely on the configurations of bosons in excited states, implying zero entropy for particles in the ground state. When two such systems merge, the resulting entropy is less than the sum of the individual entropies. This entropy decrease is numerically shown to arise from an effectively but anomalous exchange of particles in excited states, where $\overline{N}!/(\overline{N}_{1}!\overline{N}_{2}!)<1$. Here, $\overline{N}$, $\overline{N}_{1}$, and $\overline{N}_{2}$ are real decimals representing, respectively, the mean number of particles in excited states in the merged system and the two individual systems before merging, with $\overline{N}<\overline{N}_{1}+\overline{N}_{2}$.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic pressure and mechanical pressure for electromagnetic media

By the mechanical pressure we mean that the pressure in the fundamental thermodynamic equation with the naive form of the electromagnetic work used, while the thermodynamic one we mean that in the equation with proper thermodynamic form of the electromagnetic work instead. Both pressures differ from a magnetic mutual field pressure which results from the electromagnetic stress tensor for the linear and uniform media in static electromagnetic field. Both pressures are in essence tensors, but a quasi-scalar theory is sufficient for the simple media.

physics.class-ph↗

arXiv2024

The vanishing of heat capacity as thermodynamic third law implies existence of singular systems

A corollary of the third law of thermodynamics is that the heat capacities of a system approach zero as the temperature approaches absolute zero Kevin. Many have attempted to take the corollary as the third law, but two counterexamples has been constructed explicitly. We present a theorem that the vanishing of heat capacity as the third law implies an existence of singular systems, and two known counterexamples are illustrations of the theorem.

cond-mat.stat-mech↗

arXiv2024

Intermittent emission of particles from a Bose-Einstein condensate in a one-dimensional lattice

We investigate particle emission from a Bose-Einstein condensate with periodically modulated interactions in a one-dimensional lattice. Within perturbative analysis, which leads to instabilities for discrete modes, we obtain the main regimes where the system can emit a large particle jet, and find that the emission is distinctly intermittent rather than continuous. The time evolution of the trapped particles exhibits a stair-like decay, and a larger drive induces a more significant intermittency. We further shed light on the dynamics of the stimulating process, and demonstrate that instead of a real suspension, the intermittency represents a build-up stage of the system. The theoretical framework might be generalized to the explorations on multiple-site systems with analogous configurations and couplings, and offer new insights into other fundamental nonequilibrium problems.

cond-mat.quant-gas↗

arXiv2023

On relation between renormalized frequency and heat capacity for particles in an anharmonic potential

For free particles in a simple harmonic potential plus a weak anharmonicity, characterized by a set of anharmonic parameters, Newtonian mechanics asserts that there is a renormalization of the natural frequency of the periodic motion; and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas in the anharmonic potential. The orbital motion and thermal motion depend on the same anharmonic parameters, but in different combinations. These two manners of combinations are fundamentally different, demonstrating that statistical law can not emerge from the many-body limit of deterministic law for one-body.

cond-mat.stat-mech↗

arXiv2023

A correspondence from renormalized frequency to heat capacity for particles in an anharmonic potential

For particles in an anharmonic potential, classical mechanics asserts that there is a renormalization of the bare frequency of the oscillatory motion, and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas composed of particles in the anharmonic potential. When the frequency and the heat capacity are expressed in perturbative series, respective, in terms of the characteristic lengths in mechanics and statistical physics, the expansion coefficients have an order-by-order correspondence. This correspondence is in contrast to our intuition that the renormalized frequency enters the statistical mechanics as a single quantity.

cond-mat.stat-mech↗

arXiv2021

Asynchronous finite differences in most probable distribution with finite numbers of particles

For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. If $f\left( x\right) $ is a sum of two such functions $f\left( x\right) =f_{1}\left( x\right) +f_{2}\left( x\right) $, the first order difference of $Δf\left( x\right) $ can be grouped into four possible combinations, in which two are the usual synchronous ones $Δ^{f}f_{1}\left( x\right) +Δ^{f}f_{2}\left( x\right) $ and $Δ^{b}f_{1}\left( x\right) +Δ^{b}f_{2}\left( x\right) $, and other two are asynchronous ones $Δ^{f}f_{1}\left( x\right) +Δ^{b}f_{2}\left( x\right) $ and $Δ^{b}f_{1}\left( x\right) +Δ^{f}f_{2}\left( x\right) $, where $Δ^{f}$ and $Δ^{b}$ denotes the forward and backward difference respectively. Thus, the first order variation equation $Δf\left( x\right) =0$ for this function $f\left( x\right) $ gives at most four different solutions which contain both true and false one. \emph{A formalism of the discrete calculus of variations is developed to single out the true one by means of comparison of the second order variations, in which the largest value in magnitude indicates the true solution, yielding the exact form of the distributions for Boltzmann, Bose and Fermi system without requiring the numbers of particle to be infinitely large}. When there is only one particle in the system, all distributions reduce to be the Boltzmann one.

cond-mat.stat-mech↗

arXiv2021

Geometrical aspect of susceptibility critical exponent

Critical exponent $γ\succeq 1.1$ characterizes behavior of the mechanical susceptibility of a real fluid when temperature approaches the critical one. It results in zero Gaussian curvature of the local shape of the critical point on the thermodynamic equation of state surface, which imposes a new constraint upon the construction of the potential equation of state of the real fluid from the empirical data. All known empirical equations of state suffer from a weakness that the Gaussian curvature of the critical point is negative definite instead of zero.

cond-mat.stat-mech↗

arXiv2021

Local shape of the vapor-liquid critical point on the thermodynamic surface and the van der Waals equation of state

Differential geometry is powerful tool to analyze the vapor-liquid critical point on the surface of the thermodynamic equation of state. The existence of usual condition of the critical point $\left( \partial p/\partial V\right) _{T}=0$ requires the isothermal process, but the universality of the critical point is its independence of whatever process is taken, and so we can assume $\left( \partial p/\partial T\right) _{V}=0$. The distinction between the critical point and other points on the surface leads us to further assume that the critical point is geometrically represented by zero Gaussian curvature. A slight extension of the van der Waals equation of state is to letting two parameters $a$ and $b$ in it vary with temperature, which then satisfies both assumptions and reproduces its usual form when the temperature is approximately the critical one.

cond-mat.stat-mech↗

arXiv2021

The curvature-induced gauge potential and the geometric momentum for a particle on a hypersphere

A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences a curvature-induced gauge potential, whose form was given long ago (J. Math. Phys. \textbf{34}(1993)2827). We demonstrate that the momentum for the particle on the hypersphere is the geometric one including the gauge potential and its components obey the commutation relations $\left[ p_{i},p_{j}\right] =-i\hbar J_{ij}/r^{2}$, in which $\hbar $ is the Planck's constant, and $p_{i}$ ($i,j=1,2,3,...N$) denotes the $i-$th component of the geometric momentum, and $J_{ij}$ specifies the $ij-$th component of the generalized\textit{\ angular momentum} containing both the orbital part and the coupling of the generators of continuous rotational symmetry group $% SO(N-1)$ and curvature, and $r$ denotes the radius of the $N-1$ dimensional hypersphere.

hep-th↗

arXiv2021

A new discrete calculus of variations and its applications in statistical physics

For a discrete function $f\left( x\right) $ on a discrete set, the finite difference can be either forward and backward. However, we observe that if $ f\left( x\right) $ is a sum of two functions $f\left( x\right) =f_{1}\left( x\right) +f_{2}\left( x\right) $ defined on the discrete set, the first order difference of $Δf\left( x\right) $ is equivocal for we may have $ Δ^{f}f_{1}\left( x\right) +Δ^{b}f_{2}\left( x\right) $ where $ Δ^{f}$ and $Δ^{b}$ denotes the forward and backward difference respectively. Thus, the first order variation equation for this function $ f\left( x\right) $ gives many solutions which include both true and false one. A proper formalism of the discrete calculus of variations is proposed to single out the true one by examination of the second order variations, and is capable of yielding the exact form of the distributions for Boltzmann, Bose and Fermi system without requiring the numbers of particle to be infinitely large. The advantage and peculiarity of our formalism are explicitly illustrated by the derivation of the Bose distribution.

physics.gen-ph↗

arXiv2021

Discrete calculus of variations and Boltzmann distribution without Stirling's approximation

A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most probable distribution for the Boltzmann system is then reproduced without the Stirling's approximation, and free from other theoretical problems.

cond-mat.stat-mech↗

arXiv2020

Breakdown of equipartition of energy for vibrational heat capacity of diatomic molecular gas due to nonvanishing bond length

When the theorem of equipartition of energy applies to the vibrational degree of freedom within diatomic molecular gas, the bond length is usually taken as zero so that the theorem is valid. Once the bond length is taken into consideration, calculations show that the mean energy of the vibrational heat capacity will significantly deviate from the standard value near the high temperature which breaks down the bond.

cond-mat.stat-mech↗

arXiv2020

Fastest Frozen Temperature for a Thermodynamic System

For a thermodynamic system obeying both the equipartition theorem in high temperature and the third law in low temperature, the curve showing relationship between the specific heat and the temperature has two common behaviors:\ it terminates at zero when the temperature is zero Kelvin and converges to a constant as temperature is higher and higher. Since it is always possible to find the characteristic temperature $T_{C}$ to mark the excited temperature as the specific heat almost reaches the equipartition value, it is reasonable to find a temperature in low temperature interval, complementary to $T_{C}$. The present study reports a possibly universal existence of the such a temperature $\vartheta$, defined by that at which the specific heat falls \textit{fastest} along with decrease of the temperature. For the Debye model of solids, above the temperature $\vartheta$ the Debye's law starts to fail.

cond-mat.stat-mech↗

arXiv2019

No existence of the geometric potential for a Dirac fermion on two-dimensional curved surfaces of revolution

For a free particle that non-relativistically moves on a curved surface, there are curvature-induced quantum potentials that significantly influence the surface quantum states, but the experimental results in topological insulators, whenever curved or not, indicate no evidence of such a potential, implying that there does not exist such a quantum potential for the relativistic particles, constrained on the surface or not. Within the framework of Dirac quantization scheme, we demonstrate a general result that for a Dirac fermion on a two-dimensional curved surface of revolution, no curvature-induced quantum potential is permissible.

cond-mat.mes-hall↗

arXiv2019

Charge nonconservation of molecular devices in the presence of a nonlocal potential

In the presence of a nonlocal potential in molecular device systems, generally the charge conservation cannot be satisfied, and in literatures the modifications of the conventional definition of current were given to solve this problem. We demonstrate that, however, the nonconservation is not due to the invalidation of the conventional definition of current, but originates respectively from the improper approximations to electron-electron interactions and the inappropriate definition of current using pseudo wave functions in pseudopotential implementations. In this work, we propose a nonlocal-potential formulation of the interactions to fulfill the charge conservation and also give a discussion about the calculation of current when the pseudopotential is involved. As an example of application of our formulation, we further present the calculated results of a double-barrier model.

cond-mat.mes-hall↗

arXiv2019

Curvature-induced noncommutativity of two different components of momentum for a particle on a hypersurface

As a nonrelativistic particle constrained to remain on an $N-1$ ($N\geq 2$) dimensional hypersurface embedded in an $N$ dimensional Euclidean space, two different components $p_{i}$ and $p_{j}$ ($i,j=1,2,3,...N$) of the Cartesian momentum of the particle are not mutually commutative, and explicitly commutation relations $[p_{i},p_{j}]\left( \neq 0\right) $ depend on products of positions and momenta in uncontrollable ways. The \textit{% generalized} Dupin indicatrix of the hypersurface, a local analysis technique, is utilized to explore the dependence of the noncommutativity on the curvatures on a \textit{local point }of the hypersurface. The first finding is that the noncommutativity can be grouped into two categories; one is the product of a sectional curvature and the angular momentum, and another is the product of a principal curvature and the momentum. The second finding is that, for a small circle lying a \textit{tangential plane} covering the \textit{local point}, the noncommutativity leads to a rotation operator and the amount of the rotation is an angle anholonomy; and along each of the \textit{normal sectional curves} centering the \textit{given point} the noncommutativity leads to a translation plus an additional rotation and the amount of the rotation is one half of the tangential angle change of the arc.

physics.gen-ph↗