Maximally-localized position, Euclidean path-integral, and thermodynamics in GUP quantum mechanics

Bernardo, Reginald Christian; Esguerra, Jose Perico

doi:10.1016/j.aop.2018.02.015

Cited by 12 publications

(10 citation statements)

References 59 publications

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“…Implications of theories with a fundamental length are often addressed by deforming the Heisenberg Uncertainty Principle (HUP) in such a way as to accommodate a minimum uncertainty in position at Planck scale. The ensuing relation, commonly known as Generalized Uncertainty Principle (GUP), has been studied in a variety of contexts, ranging from quantum theory [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], to black hole physics [31][32][33][34][35][36][37][38][39][40][41][42][43][44] and cosmology [45,46]. Potential effects of a modified Heisenberg algebra have also been explored in graphene [47], where the minimal length is provided by the honeycomb lattice spacing.…”

Section: Introductionmentioning

confidence: 99%

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Bosso

Luciano

2021

Eur. Phys. J. C

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Several models of quantum gravity predict the emergence of a minimal length at Planck scale. This is commonly taken into consideration by modifying the Heisenberg uncertainty principle into the generalized uncertainty principle. In this work, we study the implications of a polynomial generalized uncertainty principle on the harmonic oscillator. We revisit both the analytic and algebraic methods, deriving the exact form of the generalized Heisenberg algebra in terms of the new position and momentum operators. We show that the energy spectrum and eigenfunctions are affected in a non-trivial way. Furthermore, a new set of ladder operators is derived which factorize the Hamiltonian exactly. The above formalism is finally exploited to construct a quantum field theoretic toy model based on the generalized uncertainty principle.

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Section: Introductionmentioning

confidence: 99%

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Bosso

Luciano

2021

Eur. Phys. J. C

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“…Vice-versa, the commutator ( 5 ) implies the inequality ( 4 ) for any state. The GUP is widely studied in the context of quantum mechanics [ 25 – 27 ], quantum field theory [ 28 ], quantum gravity [ 29 , 30 ], and for various deformations of the quantization rules [ 29 – 31 ].…”

Section: Introductionmentioning

confidence: 99%

Modified Unruh effect from generalized uncertainty principle

et al. 2018

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We consider a generalized uncertainty principle (GUP) corresponding to a deformation of the fundamental commutator obtained by adding a term quadratic in the momentum. From this GUP, we compute corrections to the Unruh effect and related Unruh temperature, by first following a heuristic derivation, and then a more standard field theoretic calculation. In the limit of small deformations, we recover the thermal character of the Unruh radiation. Corrections to the temperature at first order in the deforming parameter are compared for the two approaches, and found to be in agreement as for the dependence on the cubic power of the acceleration of the reference frame. The dependence of the shifted temperature on the frequency is also pointed out and discussed.

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“…which, together with (2), satisfy Jacobi identities and determine the whole symplectic structure of the model. So far, the quadratic GUP (1) has been mostly used to study phenomenology of quantum gravity in many sectors, ranging from quantum mechanics [9,10,11] to particle physics [12,13,14,15] and cosmology [16,17]. In contrast, comparatively less research has been conducted on the quasi-classical domain of the GUP.…”

Section: Introductionmentioning

confidence: 99%

Coherent states for generalized uncertainty relations and their cosmological implications

Jizba

Lambiase

Luciano

et al. 2023

J. Phys.: Conf. Ser.

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We study coherent states associated with a generalized uncertainty principle (GUP). Our particular focus is on the negative deformation parameter β. We show that the ensuing coherent state can be identified with Tsallis’ probability amplitude with the non-extensivity parameter q being a monotonically increasing function of β. Furthermore, for β < 0, we reformulate the GUP in terms of a one-parameter class of Tsallis entropy based uncertainty relations, which are again saturated by the GUP coherent states. We argue that this combination of coherent states with Tsallis entropy offers a natural conceptual framework allowing to study the quasi-classical regime of GUP in terms of non-extensive thermostatistics. We bolster this claim by discussing a generalization of Verlinde’s entropic force and the ensuing implications in the late-inflation epoch. The corresponding dependence of the β parameter on the cosmological time is derived for the reheating epoch. The obtained β is consistent with both values predicted by string-theory models and the naturalness principle.

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Maximally-localized position, Euclidean path-integral, and thermodynamics in GUP quantum mechanics

Cited by 12 publications

References 59 publications

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Generalized uncertainty principle: from the harmonic oscillator to a QFT toy model

Modified Unruh effect from generalized uncertainty principle

Coherent states for generalized uncertainty relations and their cosmological implications

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