Electron energy spectrum of a finite crystals in a uniform electric field

Berezhkovskii, Alexander M.; Овчинников, А. А.

doi:10.1002/pssb.2220850112

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Such a discrete spectrum has been dubbed a Wannier-Stark ladder [49][50][51]. The fate of these ladders on finite samples has been investigated by several authors in the 1970s [52][53][54][55][56][57]. In order to investigate the behavior of T in the various regimes of system size N and applied electric field F, we have to thoroughly revisit these works.…”

Section: A Tight-binding Particle On An Electrified Chainmentioning

confidence: 99%

Equilibration properties of small quantum systems: further examples

Luck¹

2017

J. Phys. A: Math. Theor.

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It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace T of this matrix measures the degree of equilibration of the system prepared in a typical state of the preferential basis. This quantity may vary between unity (ideal equilibration) and the dimension N of the Hilbert space (no equilibration at all). Here we analyze several examples of simple systems where the behavior of T can be investigated by analytical means. We first study the statistics of T when the Hamiltonian governing the dynamics is random and drawn from a distribution invariant under the group U(N ) or O(N ). We then investigate a quantum spin S in a tilted magnetic field making an arbitrary angle with the preferred quantization axis, as well as a tight-binding particle on a finite electrified chain. The last two cases provide examples of the interesting situation where varying a system parameter -such as the tilt angle or the electric field -through some scaling regime induces a continuous transition from good to bad equilibration properties.

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Section: A Tight-binding Particle On An Electrified Chainmentioning

confidence: 99%

Equilibration properties of small quantum systems: further examples

Luck¹

2017

J. Phys. A: Math. Theor.

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A study of Stark ladders in finite crystals on the basis of the tight-binding approximation

Roy

Mahapatra

1984

J. Phys. C: Solid State Phys.

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Equilibration properties of small quantum systems: further examples

Luck

2017

Preprint

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It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace T of this matrix measures the degree of equilibration of the system prepared in a typical state of the preferential basis. This quantity may vary between unity (ideal equilibration) and the dimension N of the Hilbert space (no equilibration at all). Here we analyze several examples of simple systems where the behavior of T can be investigated by analytical means. We first study the statistics of T when the Hamiltonian governing the dynamics is random and drawn from a distribution invariant under the group U(N ) or O(N ). We then investigate a quantum spin S in a tilted magnetic field making an arbitrary angle with the preferred quantization axis, as well as a tight-binding particle on a finite electrified chain. The last two cases provide examples of the interesting situation where varying a system parameter -such as the tilt angle or the electric field -through some scaling regime induces a continuous crossover from good to bad equilibration properties.

show abstract

Electron energy spectrum of a finite crystals in a uniform electric field

Cited by 3 publications

References 13 publications

Equilibration properties of small quantum systems: further examples

Equilibration properties of small quantum systems: further examples

A study of Stark ladders in finite crystals on the basis of the tight-binding approximation

Equilibration properties of small quantum systems: further examples

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