Deformation Quantization for Coupled Harmonic Oscillators on a General Noncommutative Space

Lin, Bing-Sheng; Jing, Sicong; Heng, Tai-Hua

doi:10.1142/s0217732308023992

Cited by 9 publications

(8 citation statements)

References 22 publications

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“…Instead one can consider the Wigner functions of the system. By virtue of deformation quantization method, one can derive the Wigner functions and energy spectra of the system in the noncommutative phase space [38]. In noncommutative phase space, the Hamiltonian and the corresponding Wigner functions W satisfy the so-called * −genvalue equation…”

Section: Wigner Functions Of Harmonic Oscillators In Noncommutative P...mentioning

confidence: 99%

“…The von Neumann entropy is defined by the density operators. Since we consider the physical system in noncommutative phase space (NCPS) in the present work, it is convenient to use the Wigner functions to calculate the entropy of the system [38]. There are some types of quantum entropy defined by the Wigner functions in phase space [39]- [43].…”

Section: Introductionmentioning

confidence: 99%

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Induced entanglement entropy of harmonic oscillators in non-commutative phase space

Lin

Heng

2019

Mod. Phys. Lett. A

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We study the quantum entropy and entanglement of the 2D isotropic harmonic oscillators in noncommutative phase space. We propose a definition of quantum Rényi entropy by the Wigner functions in noncommutative phase space. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the harmonic oscillators. We find that the 2D isotropic harmonic oscillators can be entangled in noncommutative phase space. This is an entanglement-like effect caused by the noncommutativity of the phase space. We also study the Tsallis entropy of the harmonic oscillators in noncommutative phase space.

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Section: Wigner Functions Of Harmonic Oscillators In Noncommutative P...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Induced entanglement entropy of harmonic oscillators in non-commutative phase space

Lin

Heng

2019

Mod. Phys. Lett. A

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“…We will examine two coupled harmonic oscillator (HO) [45,46] specified by the coordinates x 1 , x 2 and masses m 1 , m 2 . One can describe this using the Hamiltonian as the sum of free and interacting parts…”

Section: Coupled Harmonic Oscillatormentioning

confidence: 99%

Non-commutative space engine: a boost to thermodynamic processes

Pandit,

Chattopadhyay,

Paul

2019

Preprint

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We introduce quantum heat engines that perform quantum Otto cycle and the quantum Stirling cycle by using a coupled harmonic oscillator as its working substance. In the quantum regime, different working medium is considered for the analysis of the engine models to boost the efficiency of the cycles. In this work, we present Otto and Stirling cycle in the quantum realm where the phase space is non-commutative in nature. By using the notion of quantum thermodynamics we develop the thermodynamic variables in non-commutative phase space. We encounter a catalytic effect on the efficiency of the engine in non-commutative space (i.e, we encounter that the Stirling cycle reaches near to the efficiency of the ideal cycle) when compared with the commutative space. Moreover, we obtained a notion that the working medium is much more effective for the analysis of the Stirling cycle than that of the Otto cycle.

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“…Recently experiments with micro-and nano-oscillators were implemented for probing minimal length [49]. In noncommutative space of canonical type two coupled harmonic oscillators were studied in [50,51,52]. In [53] a spectrum of a system of N oscillators interacting with each other (symmetric network of coupled harmonic oscillators) has been examined in rotationally invariant noncommutative phase space.…”

Section: Introductionmentioning

confidence: 99%

Harmonic Oscillator Chain in Noncommutative Phase Space with Rotational Symmetry

Gnatenko

2019

Ukr. J. Phys.

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We consider a quantum space with rotationally invariant noncommutative algebra of coordinates and momenta. The algebra contains tensors of noncommutativity constructed involving additional coordinates and momenta. In the rotationally invariant noncommutative phase space harmonic oscillator chain is studied. We obtain that noncommutativity affects on the frequencies of the system. In the case of a chain of particles with harmonic oscillator interaction we conclude that because of momentum noncommutativity the spectrum of the center-of-mass of the system is discrete and corresponds to the spectrum of harmonic oscillator.

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Deformation Quantization for Coupled Harmonic Oscillators on a General Noncommutative Space

Cited by 9 publications

References 22 publications

Induced entanglement entropy of harmonic oscillators in non-commutative phase space

Induced entanglement entropy of harmonic oscillators in non-commutative phase space

Non-commutative space engine: a boost to thermodynamic processes

Harmonic Oscillator Chain in Noncommutative Phase Space with Rotational Symmetry

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