δ‐function perturbations and boundary problems by path integration

Grosche, Christian

doi:10.1002/andp.19935050606

Cited by 37 publications

(34 citation statements)

References 61 publications

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“…The retarded Green-function can be calculated recursively [8]. Adding a new impurity to a system with L impurities changes the Green-function the following way…”

Section: Of the Systemmentioning

confidence: 99%

Crossover from regular to chaotic behavior in the conductance of periodic quantum chains

1998

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The conductance of a waveguide containing finite number of periodically placed identical point-like impurities is investigated. It has been calculated as a function of both the impurity strength and the number of impurities using the Landauer-Büttiker formula. In the case of few impurities the conductance is proportional to the number of the open channels N of the empty waveguide and shows a regular staircase like behavior with step heights ≈ 2e 2 /h. For large number of impurities the influence of the band structure of the infinite periodic chain can be observed and the conductance is approximately the number of energy bands (smaller than N ) times the universal constant 2e 2 /h. This lower value is reached exponentially with increasing number of impurities. As the strength of the impurity is increased the system passes from integrable to quantum-chaotic. The conductance, in units of 2e 2 /h, changes from N corresponding to the empty waveguide to ∼ N/2 corresponding to chaotic or disordered system. It turnes out, that the conductance can be expressed as (1 − c/2)N where the parameter 0 < c < 1 measures the chaoticity

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“…The retarded Green-function can be calculated recursively [8]. Adding a new impurity to a system with L impurities changes the Green-function the following way…”

Section: Of the Systemmentioning

confidence: 99%

Crossover from regular to chaotic behavior in the conductance of periodic quantum chains

1998

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“…, where the system is being "squeezed" into a narrow shell a ≤ η ≤ b, simulating the quantization on a hyper-surface in the limit a → b in a manner similar to [4] (see the equation 2.15 in [4]), but the detailed analysis will be published elsewhere.…”

Section: Discussionmentioning

confidence: 99%

On the Green function of linear evolution equations for a region with a boundary

Krylov

Robnik

1999

J. Phys. A: Math. Gen.

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“…The denominator in the final expression is obtained from a factor (λ + α)(λ + α) in the denominator that arises from the exponent (2.17) in the generalized zero mode integral (2.13) on the one hand, and a factor ofλ + α in the numerator from the z-derivative of the angular variable θ on the other hand (arising from the zero mode lifting term (2.10)). Multiplying these, we find the final formula 20) which is the compact lattice sum form [8] of the cigar elliptic genus. We have given a direct derivation of the lattice sum form, using the non-linear sigma model description.…”

Section: The Lattice Summentioning

confidence: 99%

“…What follows is a review of the results derived in e.g. [18][19][20], albeit from an original perspective.…”

Section: Quantum Mechanics On a Half Linementioning

confidence: 99%

An elliptic triptych

Troost

2017

J. High Energ. Phys.

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Abstract:We clarify three aspects of non-compact elliptic genera. Firstly, we give a path integral derivation of the elliptic genus of the cigar conformal field theory from its non-linear sigma-model description. The result is a manifestly modular sum over a lattice. Secondly, we discuss supersymmetric quantum mechanics with a continuous spectrum. We regulate the theory and analyze the dependence on the temperature of the trace weighted by the fermion number. The dependence is dictated by the regulator. From a detailed analysis of the dependence on the infrared boundary conditions, we argue that in noncompact elliptic genera right-moving supersymmetry combined with modular covariance is anomalous. Thirdly, we further clarify the relation between the flat space elliptic genus and the infinite level limit of the cigar elliptic genus.

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δ‐function perturbations and boundary problems by path integration

Cited by 37 publications

References 61 publications

Crossover from regular to chaotic behavior in the conductance of periodic quantum chains

Crossover from regular to chaotic behavior in the conductance of periodic quantum chains

On the Green function of linear evolution equations for a region with a boundary

An elliptic triptych

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