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arXiv:0909.3775 · Modern Physics Letters B

STATISTICS OF A FREE SINGLE QUANTUM PARTICLE AT A FINITE TEMPERATURE

Jianping Peng

Published Sep 17, 2010• 3 citations
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Abstract

We present a model to study the statistics of a single structureless quantum particle freely moving in a space at a finite temperature. It is shown that the quantum particle, in response to the temperature, can exchange energy with its environment in the form of heat transfer. The underlying mechanism is diffraction at the edge of the wavefront of its matter wave. The expressions of energy and entropy of the particle are obtained for the irreversible process.

DOI
10.1142/s0217984910024912

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We present a model to study the statistics of a single structureless quantum particle freely moving in a space at a finite temperature. It is shown that the quantum particle, in response to the temperature, can exchange energy with its environment in the form of heat transfer. The underlying mechanism is diffraction at the edge of the wavefront of its matter wave. The expressions of energy and entropy of the particle are obtained for the irreversible process.
We analyze the heat exchange distribution of open quantum systems undergoing a thermal relaxation process with a time-dependent effective temperature. We show that such processes arise, for example, if the dynamics maximizes the entropy production. Using a two-point measurement scheme, we find an expression for the heat moment generating function that depends solely on the system's partition function and on the thermalization function (i.e., the law of cooling) describing the effective temperature. Applications include the relaxation of free bosonic and fermionic modes, for which closed-form expressions for the time-dependent heat distribution function are derived. Multiple free modes with arbitrary dispersion relations are also briefly discussed. In the semiclassical limit our formula agrees with previous results of the literature for the heat distribution of an optically trapped nanoscopic particle far from equilibrium.
Experimental data and the principles of quantum mechanics suggest that a crystal is a condensate of `wavicles' enclosed in a box, where `wavicle' denotes the indefinite wave-particle status of the microscopic constituents. When it is not perturbed the crystal is in a classical-like state. The wavefunction, the internal energy and the entropy are all of them equal to zero. The thermodynamic temperature is indefinite. Perturbations via energy- and/or momentum-transfer reveal quantum effects. The temperature laws for the heat capacities of some hydrogen-bonded crystals are rationalized with superposition states depending on the quantum temperature which is crystal-dependent. Heat-transfer is a coherent anentropic process. Apart from energy conservation, the other laws of thermodynamics are irrelevant.
In this paper, we investigate theoretically a dilute stream of free quantum particles passing through a macroscopic circular aperture of matter-waves and then moving in a space at a finite temperature, taking into account the dissipative coupling with the environment. The portion of particles captured by the detection screen is studied by varying the distance between the aperture and the screen. Depending on the wavelength, the temperature, and the dimension of the aperture, an unusual local valley-peak structure is found in increasing the distance, in contrast to traditional thinking that it decreases monotonically. The underlying mechanism is the nonlocality in the process of decoherence for an individual particle.