Grassmann integration in stochastic quantum physics: The case of compound-nucleus scattering

Verbaarschot, J. J. M.; Weidenmüller, H. A.; Zirnbauer, Martin R.

doi:10.1016/0370-1573(85)90070-5

Cited by 805 publications

(1,167 citation statements)

References 18 publications

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“…The matrices T parameterize the coset space UOSP(1, 1/1, 1)/[UOSP(1, 1)⊗UOSP(1, 1)], and σ (0) is a diagonal supermatrix of dimension four with entries given by Eq. (29) in the usual way [34]. Using this and the saddle-point solution in the expression of the effective Lagrangean, the first-order term in ǫ takes the canonical form…”

Section: Saddle Pointmentioning

confidence: 99%

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Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

et al. 2002

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We consider m spinless Bosons distributed over l degenerate singleparticle states and interacting through a k-body random interaction with Gaussian probability distribution (the Bosonic embedded k-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as l → ∞ or as m → ∞. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit l → ∞ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as m → ∞ with both k and l fixed. Here we show that the ensemble is not ergodic, and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency towards * Present address:

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Section: Saddle Pointmentioning

confidence: 99%

“…[34]) distinguishes the retarded and advanced cases. The argument also carries through for higher-point correlation functions.…”

Section: Saddle Pointmentioning

confidence: 99%

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

et al. 2002

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“…The level spacings exhibit fluctuations and therefore one expects that the inverse compressibility of different samples, as well as the inverse compressibility for the same sample at different chemical potentials, will also exhibit fluctuations of order of the single-electron mean level spacing ∆. In the non-interacting regime there are many theoretical approaches which can be used to calculate these fluctuations, among them are the random matrix theory (RMT) [9], perturbative diagrammatic calculations [8] and the supersymmetry method [10,11].…”

Section: Introductionmentioning

confidence: 99%

Compressibility, capacitance, and ground-state energy fluctuations in a weakly interacting quantum dot

Berkovits

Altshuler²

1997

Phys. Rev. B

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We study the effect of electron-electron (e-e) interactions on compressibility, capacitance and inverse compressibility of electrons in a quantum dot or a small metallic grain. The calculation is performed in the random-phase approximation. As expected, the ensemble-averaged compressibility and capacitance decreases as a function of the interaction strength, while the mean inverse compressibility increases. Fluctuations of the compressibility are found to be strongly suppressed by the e-e interactions. Fluctuations of the capacitance and inverse compressibility also turn out to be much smaller than their averages. The analytical calculations are compared with the results of a numerical calculation for the inverse compressibility of a disordered tight-binding model. Excellent agreement for weak interaction values is found. Implications for the interpretation of current experimental data are discussed.

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“…It prevents a straightforward calculation of the Lamb shift and reminds to proposition 13 in Feynman's famous article [43]. It is here where statistical considerations [44] can perhaps be implemented in the future. The next severe approximation resides in Eq.…”

Section: Summary and Discussionmentioning

confidence: 99%

On confinement in a light-cone Hamiltonian for QCD

Pauli¹

1999

Eur. Phys. J. C

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Abstract. The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the qq-space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fockspace regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement.

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Grassmann integration in stochastic quantum physics: The case of compound-nucleus scattering

Cited by 805 publications

References 18 publications

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

Compressibility, capacitance, and ground-state energy fluctuations in a weakly interacting quantum dot

On confinement in a light-cone Hamiltonian for QCD

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