Deformed quantum mechanics and<i>q</i>-Hermitian operators

Lavagno, Andrea

doi:10.1088/1751-8113/41/24/244014

Cited by 34 publications

(23 citation statements)

References 39 publications

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“…The thermodynamic functions such as entropy, pressure, internal energy, specific heat etc. of such deformed systems have been studied and compared with standard bosons and fermions [11,12,13,14,15,16,17,18,19,20]. The method of detailed balance may be employed for the purpose of establishing an intermediate statistics and this is known to require the use of basic numbers or bracket numbers.…”

Section: Introductionmentioning

confidence: 99%

Intermediate statistics as a consequence of deformed algebra

Lavagno

Swamy

2010

Physica A: Statistical Mechanics and its Applications

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We present a formulation of the deformed oscillator algebra which leads to intermediate statistics as a continuous interpolation between the Bose-Einstein and Fermi-Dirac statistics. It is deduced that a generalized permutation or exchange symmetry leads to the introduction of the basic number and it is then established that this in turn leads to the deformed algebra of oscillators. We obtain the mean occupation number describing the particles obeying intermediate statistics which thus establishes the interpolating statistics and describe boson like and fermion like particles obeying intermediate statistics. We also obtain an expression for the mean occupation number in terms of an infinite continued fraction, thus clarifying successive approximations.Comment: 18 pages, to appear in Physica

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Section: Introductionmentioning

confidence: 99%

Intermediate statistics as a consequence of deformed algebra

Lavagno

Swamy

2010

Physica A: Statistical Mechanics and its Applications

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“…Furthermore, it is remarkable to observe that the q-calculus, based on the so-called Jackson Derivative (JD) operator and its inverse operator q-integral, is indeed well suited for describing fractal and multifractal systems. As soon as the system exhibits a discrete-scale invariance, the natural tool is provided by Jackson q-derivative and q-integral, which constitute the natural generalization of the regular derivative and integral for discretely self-similar systems [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Thermostatistics of Deformed Bosons and Fermions

Lavagno

Swamy

2009

Found Phys

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Based on the q-deformed oscillator algebra, we study the behavior of the mean occupation number and its analogies with intermediate statistics and we obtain an expression in terms of an infinite continued fraction, thus clarifying successive approximations. In this framework, we study the thermostatistics of q-deformed bosons and fermions and show that thermodynamics can be built on the formalism of qcalculus. The entire structure of thermodynamics is preserved if ordinary derivatives are replaced by the use of an appropriate Jackson derivative and q-integral. Moreover, we derive the most important thermodynamic functions and we study the q-boson and q-fermion ideal gas in the thermodynamic limit.

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“…The information of the 2-qubit system is investigated within the magnetic field, non-Markovian environments, and acceleration [4,5,6]. On the other hand, the q-deformed of the Heisenberg algebra has many physical applications [7,8,9,10,11]. Lavagno [7] has obtained a generalized differential form of linear Schrödinger equation which involves the q-deformed Hamiltonian that is non-Hermitian.…”

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confidence: 99%

“…On the other hand, the q-deformed of the Heisenberg algebra has many physical applications [7,8,9,10,11]. Lavagno [7] has obtained a generalized differential form of linear Schrödinger equation which involves the q-deformed Hamiltonian that is non-Hermitian. The geometry of the q-deformed phase space has investigated by Cerchiai, et.…”

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confidence: 99%

Wigner distribution function of atomic system interacts locally with a deformed cavity

Abd‐Rabbou¹,

Metwally²,

Ahmed³

et al. 2020

Preprint

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Wigner distribution function of atomic system interacts locally with a deformed cavity is discussed. It is shown that, the deformed cavity has a destructive effect on the Wigner distribution function, where it decreases as one increases the deformation strength. The upper and lower bounds of the Wigner distribution function depends on the initial state settings of atomic system (entangled/product), the initial values of the dipole-dipole interaction's and detuning parameters, and the external distribution weight and the phase angles. The possibility of suppressing the decay induced by the deformed cavity may be increased by increasing the dipole's strength or the detuning parameter. We show that the distribution angles may be considered as a control external parameters, that maximize/ minimize the Wigner distribution function. This means that by controlling on the distribution angles, one can increase the possibility of suppressing the decoherence induced by the deformed cavity.

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Deformed quantum mechanics andq-Hermitian operators

Cited by 34 publications

References 39 publications

Intermediate statistics as a consequence of deformed algebra

Intermediate statistics as a consequence of deformed algebra

Thermostatistics of Deformed Bosons and Fermions

Wigner distribution function of atomic system interacts locally with a deformed cavity

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