dorsal/arxiv
View SchemaSpectral and thermodynamical properties of systems with noncanonical commutation rules: semiclassical approach
| Authors | J. C. Flores, S. Montecinos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307001 |
| URL | https://arxiv.org/abs/quant-ph/0307001 |
Abstract
We study different quantum one dimensional systems with noncanonical commutation rule $[x,p]=i\hbar (1+sH),$ where $H$ is the one particle Hamiltonian and $s$ is a parameter. This is carried-out using semiclassical arguments and the surmise $\hbar \to \hbar (1+sE),$ where $E$ is the energy. We compute the spectrum of the potential box, the harmonic oscillator, and a more general power-law potential $| x| ^{\nu}$% . With the above surmise, and changing the size of the elementary cell in the phase space, we obtain an expression for the partition function of these systems. We calculate the first order correction in $s$ for the internal energy and heat capacity. We apply our technique to the ideal gas, the phonon gas, and to $N$ non-interacting particles with external potential like $| x| ^{\nu}$.
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"abstract": "We study different quantum one dimensional systems with noncanonical\ncommutation rule $[x,p]=i\\hbar (1+sH),$ where $H$ is the one particle\nHamiltonian and $s$ is a parameter. This is carried-out using semiclassical\narguments and the surmise $\\hbar \\to \\hbar (1+sE),$ where $E$ is the energy. We\ncompute the spectrum of the potential box, the harmonic oscillator, and a more\ngeneral power-law potential $| x| ^{\\nu}$% . With the above surmise, and\nchanging the size of the elementary cell in the phase space, we obtain an\nexpression for the partition function of these systems. We calculate the first\norder correction in $s$ for the internal energy and heat capacity. We apply our\ntechnique to the ideal gas, the phonon gas, and to $N$ non-interacting\nparticles with external potential like $| x| ^{\\nu}$.",
"arxiv_id": "quant-ph/0307001",
"authors": [
"J. C. Flores",
"S. Montecinos"
],
"categories": [
"quant-ph"
],
"title": "Spectral and thermodynamical properties of systems with noncanonical commutation rules: semiclassical approach",
"url": "https://arxiv.org/abs/quant-ph/0307001"
},
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