Random matrix ensemble with random two-body interactions in the presence of a mean field for spin-one boson systems

Deota, H. N.; Chavda, N. D.; Kota, V. K. B.; Potbhare, V.; Vyas, Manan

doi:10.1103/physreve.88.022130

Cited by 15 publications

(8 citation statements)

References 42 publications

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“…We also plan to utilize BE-GOE(1+2) ensembles with spin one degrees of freedom to study non-equilibrium dynamics of isolated finite quantum systems. A method for constructing this ensemble is given in [59] although this ensemble is more challenging, computationally as well as analytically. Attempts will also be made to obtain an analytical understanding of the significance and magnitude of the parameter κ introduced in Section 3.2.…”

Section: Discussionmentioning

confidence: 99%

Fidelity decay and entropy production in many-particle systems after random interaction quench

Haldar¹,

Chavda²,

Vyas³

et al. 2016

J. Stat. Mech.

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We analyze the effect of spin degree of freedom on fidelity decay and entropy production of a many-particle fermionic(bosonic) system in a mean-field, quenched by a random two-body interaction preserving many-particle spin S. The system Hamiltonian is represented by embedded Gaussian orthogonal ensemble (EGOE) of random matrices (for time-reversal and rotationally invariant systems) with one plus two-body interactions preserving S for fermions/bosons. EGOE are paradigmatic models to study the dynamical transition from integrability to chaos in interacting many-body quantum systems. A simple general picture, in which the variances of the eigenvalue density play a central role, is obtained for describing the short-time dynamics of fidelity decay and entropy production. Using some approximations, an EGOE formula for the time (tsat) for the onset of saturation of entropy, is also derived. These analytical EGOE results are in good agreement with numerical calculations. Moreover, both fermion and boson systems show significant spin dependence on the relaxation dynamics of the fidelity and entropy.

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Section: Discussionmentioning

confidence: 99%

Fidelity decay and entropy production in many-particle systems after random interaction quench

Haldar¹,

Chavda²,

Vyas³

et al. 2016

J. Stat. Mech.

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“…Going beyond spin‐less boson systems, very recently BEGOE for two species boson systems with a fictitious F spin‐1/2 degree of freedom [called BEGOE(1+2)‐ F ] and for a system of interacting bosons carrying spin‐one degree of freedom [called BEGOE(1+2)‐ S 1] are introduced and their spectral properties are analyzed in detail. Here, it is important to note that the F ‐spin for bosons is similar to the F ‐spin in the proton‐neutron interacting boson model ( pn IBM) of atomic nuclei .…”

Section: Introductionmentioning

confidence: 99%

Localization‐delocalization transitions in bosonic random matrix ensembles

Chavda

Kota

2017

Annalen der Physik

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Localization to delocalization transitions in eigenfunctions are studied for finite interacting boson systems by employing one-plus two-body embedded Gaussian orthogonal ensemble of random matrices [EGOE(1+2)]. In the first analysis, considered are bosonic EGOE(1+2) for two-species boson systems with a fictitious (F ) spin degree of freedom [called BEGOE(1+2)-F ]. Numerical calculations are carried out as a function of the two-body interaction strength (λ). It is shown that, in the region (defined by λ > λ c ) after the onset of Poisson to GOE transition in energy levels, the strength functions exhibit Breit-Wigner to Gaussian transition for λ > λ F k > λ c . Further, analyzing information entropy and participation ratio, it is established that there is a region defined by λ ∼ λ t where the system exhibits thermalization. The F -spin dependence of the transition markers λ F k and λ t follow from the propagator for the spectral variances. These results, well tested near the center of the spectrum and extend to the region within ±2σ to ±3σ from the center (σ 2 is the spectral variance), establish universality of the transitions generated by embedded ensembles. In the second analysis, entanglement entropy is studied for spin-less BEGOE(1+2) ensemble and shown that the results generated are close to the recently reported results for a Bose-Hubbard model.

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“…It was shown in [6,7] that the Wigner-Racah algebra of these embedding algebras will allow one to obtain analytical results for the lower order moments of the one-and two-point correlation functions in eigenvalues. Similarly, following the recent work [8,9] on BEGOEs, it is easy to recognize that the embedding algebras for BEGUE(2)-F for two-species boson systems with F -spin and BEGUE(2)-SU(3) for spin one boson systems are U(Ω)⊗SU(2) and U(Ω)⊗SU(3) respectively. The purpose of the present paper is to establish on one hand that the Wigner-Racah algebra of these embedding algebras solve the corresponding embedded unitary ensembles and on the other to generalize the formalism to any EGUE(2) with U(Ω)⊗ SU(r) embedding and generated by random two-body interaction with SU(r) symmetry.…”

Section: Introductionmentioning

confidence: 82%

Embedded Gaussian unitary ensembles with U(Ω)⊗SU(r) embedding generated by random two-body interactions with SU(r) symmetry

Vyas

Kota

2012

Journal of Mathematical Physics

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Random matrix ensemble with random two-body interactions in the presence of a mean field for spin-one boson systems

Cited by 15 publications

References 42 publications

Fidelity decay and entropy production in many-particle systems after random interaction quench

Fidelity decay and entropy production in many-particle systems after random interaction quench

Localization‐delocalization transitions in bosonic random matrix ensembles

Embedded Gaussian unitary ensembles with U(Ω)⊗SU(r) embedding generated by random two-body interactions with SU(r) symmetry

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