arXiv subjects

S. F. Xiao

Publications and source records attributed to S. F. Xiao.

6 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↗

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↗

arXiv2018

Geometric momentum and angular momentum for charge-monopole system

For a charge-monopole pair, though the definition of the orbital angular momentum is different from the usual one, and the transverse part of the momentum that includes the vector potential as an additive term turns out to be the so-called geometric momentum that is under intensive study recently. For the charge is constrained on the spherical surface with monopole at the origin, the commutation relations between all components of geometric momentum and the orbital angular momentum satisfy the $so(3,1)$ algebra. With construction of the geometrically infinitesimal displacement operator based on the geometric momentum, the $so(3,1)$ algebra implies the Aharonov-Bohm phase shift. The related problems such as charge and flux quantization are also addressed.

quant-ph↗

arXiv2018

Surface reconstruction, premelting, and collapse of open-cell nanoporous Cu via thermal annealing

We systematic investigate the collapse of a set of open-cell nanoporous Cu (np-Cu) with the same porosity and shapes, but different specific surface area, during thermal annealing, via performing large-scale molecular dynamics simulations. Surface premelting is dominated in their collapses, and surface premelting temperatures reduce linearly with the increase of specific surface area. The collapse mechanisms are different for np-Cu with different specific surface area. If the specific surface area less than a critical value ($\sim$ 2.38 nm$^{-1}$), direct surface premelting, giving rise to the transition of ligaments from solid to liquid states, is the cause to facilitate falling-down of np-Cu during thermal annealing. While surface premelting and following recrystallization, accelerating the sloughing of ligaments and annihilation of pores, is the other mechanism, as exceeding the critical specific surface area. The recrystallization occurs at the temperatures below supercooling, where liquid is instable and instantaneous. Thermal-induced surface reconstruction prompts surface premelting via facilitating local "disordering" and "chaotic" at the surface, which are the preferred sites for surface premelting.

cond-mat.mtrl-sci↗

arXiv2016

On relationship between canonical momentum and geometric momentum

Decompositing of $N+1$-dimensional gradient operator in terms of Gaussian normal coordinates $(ξ^{0},ξ^μ)$, ($μ=1,2,3,...,N$) and making the canonical momentum $P_{0}$ along the normal direction $\mathbf{n}$ to be hermitian, we obtain $\mathbf{n}P_{0}=-i\hbar\left( \mathbf{n}\partial _{0}-\mathbf{M}_{0}\right) $ with $\mathbf{M}_{0}$ denoting the mean curvature vector on the surface $ξ^{0}=const.$ The remaining part of the momentum operator lies on the surface, which is identical to the geometric one.

quant-ph↗

arXiv2014

A self-adjoint decomposition of radial momentum implies that Dirac's introduction of the operator is insightful

With acceptance of the Dirac's observation that the \textit{canonical quantization entails using Cartesian coordinates, }we examine the\textit{\ }% operator $\mathbf{e}_{r}P_{r}$ rather than $P_{r}$ itself and demonstrate that there is a decomposition of $\mathbf{e}_{r}P_{r}$ into two self-adjoint but non-commutative parts, in which one is the total momentum and another is the transverse one. This study renders the operator $P_{r}$ indirectly measurable and physically meaningful.

quant-ph↗