Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

Varga, Imre; Pipek, János

doi:10.1103/physreve.68.026202

Cited by 81 publications

(69 citation statements)

References 33 publications

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“…Before discussing the solutions of the Schroedinger equations associated to (22,23,24), our new hamiltonians deserve some comments. It is important to note that the solvability of the resulting Schroedinger equation for these hamiltonians resides completely on the existence of I (d) (which in this case means superintegrability).…”

Section: Solvable Extensions In One Two and Three Dimensionsmentioning

confidence: 99%

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Sadurní¹,

Torres²,

Seligman³

2010

J. Phys. A: Math. Theor.

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Abstract.The Dirac oscillator coupled to an external two-component field can retain its solvability, if couplings are appropriately chosen. This provides a new class of integrable systems. A simplified way of solution is given, by recasting the known solution of the Dirac oscillator into matrix form; there one notices, that a block-diagonal form arises in a Hamiltonian formulation. The blocks are two-dimensional. Choosing couplings that do not affect the block structure, these blow up the 2×2 matrices to 4×4 matrices, thus conserving solvability. The result can be cast again in covariant form. By way of example we apply this exact solution to calculate the evolution of entanglement.

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Section: Solvable Extensions In One Two and Three Dimensionsmentioning

confidence: 99%

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Sadurní¹,

Torres²,

Seligman³

2010

J. Phys. A: Math. Theor.

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“…For a revision of their properties see [38,39,40,41,42,43,44] and the reviews [45,46]. The Rényi entropies and their associated uncertainty relations have been widely used to investigate a great deal of quantum-mechanical properties and phenomena of physical systems and processes [29,45,46,44], ranging from the quantum-classical correspondence [47] and quantum entanglement [48] to pattern formation and Brown processes [49,50], fractality and chaotic systems [51,52], quantum phase transition [53] and disordered systems [54]. Moreover, the knowledge of these quantities allows us to reconstruct the corresponding probability density under certain conditions [41,55].…”

Section: Introductionmentioning

confidence: 99%

Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

et al. 2016

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Abstract. The Rényi entropies R p [ρ], p > 0, 1 of the highly-excited quantum states of the D-dimensional isotropic harmonic oscillator are analytically determined by use of the strong asymptotics of the orthogonal polynomials which control the wavefunctions of these states, the Laguerre polynomials. This Rydberg energetic region is where the transition from classical to quantum correspondence takes place. We first realize that these entropies are closely connected to the entropic moments of the quantum-mechanical probability ρ n (r) density of the Rydberg wavefunctions Ψ n,l,{µ} (r); so, to the L p -norms of the associated Laguerre polynomials. Then, we determine the asymptotics n → ∞ of these norms by use of modern techniques of approximation theory based on the strong Laguerre asymptotics. Finally, we determine the dominant term of the Rényi entropies of the Rydberg states explicitly in terms of the hyperquantum numbers (n, l), the parameter order p and the universe dimensionality D for all possible cases D ≥ 1. We find that (a) the Rényi entropy power decreases monotonically as the order p is increasing and (b) the disequilibrium (closely related to the second order Rényi entropy), which quantifies the separation of the electron distribution from equiprobability, has a quasi-Gaussian behavior in terms of D.

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“…[3,13], respectively. This type of generalization based on Rényi entropies differences was suggested in [14] after the work of Varga and Pipek [15] in this same line of thought.…”

Section: Generalized Statistical Complexity Measurecmentioning

confidence: 99%

A generalized statistical complexity measure: Applications to quantum systems

López‐Ruiz

Nagy

Romera

et al. 2009

Journal of Mathematical Physics

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A two-parameter family of complexity measuresC (α,β) based on the Rényi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the LMC complexity, which is recovered for α = 1 and β = 2. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, α or β, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator and square well. 89.75.Fb.

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Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

Cited by 81 publications

References 33 publications

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

Rényi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics

A generalized statistical complexity measure: Applications to quantum systems

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