Local currents for a deformed algebra of quantum mechanics with a fundamental length scale

AbstractThe recently developed physics of thin-film photovoltaics is suggested to be representative of other giant area electronics. We show that (i) giant-area devices are intrinsically nonuniform in the lateral directions, (ii) the nonuniformity spans length scales from millimeters to meters depending on external drivers such as light intensity and bias, and (iii) it significantly impacts the device performance. We derive a fundamental length scale that discriminates between the cases of small and large-area devices, and beyond which a new physics emerges. In addition, we present a practical method of mitigating the nonuniformity effects.

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A CLASS OF GUP SOLUTIONS IN DEFORMED QUANTUM MECHANICS

International Journal of Modern Physics D ◽

10.1142/s0218271810018153 ◽

2010 ◽

Vol 19 (12) ◽

pp. 2003-2009 ◽

Cited By ~ 50

Author(s):

POURIA PEDRAM

Keyword(s):

Black Hole ◽

Quantum Mechanics ◽

Quantum Gravity ◽

Uncertainty Principle ◽

Loop Quantum Gravity ◽

Black Hole Physics ◽

Generalized Uncertainty Principle ◽

Heisenberg Uncertainty Principle ◽

Deformed Algebra ◽

Heisenberg Uncertainty

Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to the so-called generalized uncertainty principle (GUP). This approach results from the modification of the commutation relations and changes all Hamiltonians in quantum mechanics. In this paper, we present a class of physically acceptable solutions for a general commutation relation without directly solving the corresponding generalized Schrödinger equations. These solutions satisfy the boundary conditions and exhibit the effect of the deformed algebra on the energy spectrum. We show that this procedure prevents us from doing equivalent but lengthy calculations.

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Wigner functions in quantum mechanics with a minimum length scale arising from generalized uncertainty principle

The European Physical Journal Plus ◽

10.1140/epjp/s13360-021-01166-9 ◽

2021 ◽

Vol 136 (2) ◽

Author(s):

Prathamesh Yeole ◽

Vipul Kumar ◽

Kaushik Bhattacharya

Keyword(s):

Quantum Mechanics ◽

Uncertainty Principle ◽

Generalized Uncertainty Principle ◽

Minimum Length ◽

Length Scale ◽

Wigner Functions ◽

Minimum Length Scale

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A QUANTUM-GRAVITY PERSPECTIVE ON SEMICLASSICAL vs. STRONG-QUANTUM DUALITY

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887806001685 ◽

2006 ◽

Vol 03 (07) ◽

pp. 1293-1302

Author(s):

JOSÉ M. ISIDRO

Keyword(s):

Quantum Gravity ◽

Degrees Of Freedom ◽

The Other ◽

Length Scale ◽

Specific Nature ◽

Action Integral ◽

Fundamental Length ◽

Starting Point ◽

Duality Groups ◽

Quantum Duality

It has been argued that, underlying the M-theoretic dualities, there should exist a symmetry relating the semiclassical and the strong-quantum regimes of a given action integral. On the other hand, a field-theoretic exchange between long and short distances (similar in nature to the T-duality of strings) has been shown to provide a starting point for quantum gravity, in that this exchange enforces the existence of a fundamental length scale on spacetime. In this paper, we prove that the above semiclassical vs. strong-quantum symmetry is equivalent to the exchange of long and short distances. Hence the former symmetry, as much as the latter, also enforces the existence of a length scale. We apply these facts in order to classify all possible duality groups of a given action integral on spacetime, regardless of its specific nature and of its degrees of freedom.

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QUANTUM MECHANICS AT PLANCK'S SCALE AND DENSITY MATRIX

International Journal of Modern Physics D ◽

10.1142/s0218271803003700 ◽

2003 ◽

Vol 12 (07) ◽

pp. 1265-1278 ◽

Cited By ~ 19

Author(s):

A. E. SHALYT-MARGOLIN ◽

J. G. SUAREZ

Keyword(s):

Quantum Mechanics ◽

Density Matrix ◽

Semiclassical Approximation ◽

Black Hole Entropy ◽

Uncertainty Relations ◽

Statistical Entropy ◽

Fundamental Length ◽

Definition Of ◽

Liouville’S Equation ◽

Natural Way

In this paper Quantum Mechanics with Fundamental Length is chosen as Quantum Mechanics at Planck's scale. This is possible due to the theory of General Uncertainty Relations. Here Quantum Mechanics with Fundamental Length is obtained as a deformation of Quantum Mechanics. The distinguishing feature of the proposed approach in comparison with previous ones, lies in the fact that here the density matrix are subjected to deformation, whereas in the previous approaches only commutators are deformed. The density matrix obtained by deforming the quantum-mechanical one is named the density pro-matrix throughout this paper. Within our approach two main features of Quantum Mechanics are conserved: the probabilistic interpretation of the theory and the well-known measuring procedure corresponding to that interpretation. The proposed approach allows a description of the dynamics. In particular, the explicit form of the deformed Liouville's equation and the deformed Shrödinger's picture are given. Some implications of obtained results are discussed. In particular, the problem of singularity, the hypothesis of cosmic censorship, a possible improvement of the definition of statistical entropy and the problem of information loss in black holes are considered. It is shown that the results obtained here allow one to deduce in a simple and natural way the Bekenstein–Hawking's formula for black hole entropy in semiclassical approximation.

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QUANTUM AND SEMICLASSICAL SCALES FOR THE xn ANHARMONIC OSCILLATOR

Modern Physics Letters A ◽

10.1142/s0217732392000732 ◽

1992 ◽

Vol 07 (09) ◽

pp. 763-766

Author(s):

J.T. ANDERSON

Keyword(s):

Quantum Mechanics ◽

Fine Structure ◽

Singular Point ◽

Anharmonic Oscillator ◽

Semiclassical Approximation ◽

Canonical Quantization ◽

Length Scale ◽

Quantum Invariants

The classical fine structure around a singular point has been shown to be smoothed out by h in quantum mechanics. For the xn anharmonic oscillator in the semiclassical approximation this result is shown to set a quantum length scale [Formula: see text] below which the fine structure is not observable. The length scale allows canonical quantization in terms of the ratio of the quantum to semiclassical scales [Formula: see text]. This ratio is equivalent to ratios of the quantum to semiclassical scales in action and energy and provides a measure of the departure of semiclassical from quantum invariants.

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Snyder-like modified gravity in Newton's spacetime

International Journal of Modern Physics D ◽

10.1142/s0218271818500700 ◽

2018 ◽

Vol 27 (07) ◽

pp. 1850070

Author(s):

Carlos Leiva

Keyword(s):

Modified Gravity ◽

Kepler Problem ◽

Dynamic Equations ◽

Integrals Of Motion ◽

Curved Spacetime ◽

Length Dependence ◽

Fundamental Length ◽

Deformed Algebra ◽

Torsion Free

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.

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