N. D. Chavda

Statistical properties of dense interacting boson systems with one- plus two-body random matrix ensembles

Abstract Statistical properties like nearest neighbor spacing distribution (NNSD), number of principal components (NPC), information entropy ( S info ) and number entropy ( S occu ) have been studied for interacting boson systems using one-body ( H 1 ) and an embedded GOE of two-body ( H 2 ) interactions. The NNSD for the bosonic ensembles moves steadily from Poisson to Wigner form as the 2-body interaction strength λ in the H = H 1 + λH 2 is varied. Critical strength λ C for the transition, agrees with Jacquad and Shepelyansky criterion. For NPC, S info and S occu , there is another transition point λ F , as in fermionic ensembles. Bosonic ensembles in the dense limit tend to be ergodic with increasing the number of single-particle states.

One- plus two-body random matrix ensembles for boson systems with F-spin: analysis using spectral variances

For a two-species boson system, it is possible to introduce a fictitious (F) spin for the bosons such that the two projections of F represent the two species. Then, for m bosons the total fictitious spin F takes values m/2, m/2 ? 1,?, 0 or 1/2. For such a system with m number of bosons in ? number of single-particle levels, each doubly degenerate, we introduce and analyze an embedded Gaussian orthogonal ensemble (GOE) of random matrices generated by random two-body interactions that conserve F-spin (BEGOE(1+2)-F); with degenerate single-particle levels, we have BEGOE(2)-F. Embedding algebra for BEGOE(1+2)-F ensemble is U(2?)?U(?)?SU(2) with SU(2) generating F-spin. A method for constructing the ensembles in fixed-(m, F) spaces has been developed. Numerical calculations show that for BEGOE(1+2)-F, the fixed-(m, F) density of states is close to Gaussian and level fluctuations follow the GOE in the dense limit. Similarly, generically there is Poisson to GOE transition in level fluctuations as the interaction strength (measured in the units of the average spacing of the single-particle levels defining the mean field) is increased. The interaction strength needed for the onset of the transition is found to decrease with increasing F. Formulas for the fixed-(m, F) space eigenvalue centroids and spectral variances are derived for a given member of the ensemble and also for the variance propagator for the fixed-(m, F) ensemble-averaged spectral variances. Using these, covariances in eigenvalue centroids and spectral variances are analyzed. The variance propagator clearly shows that the BEGOE(2)-F ensemble generates ground states with spin F = Fmax = m/2. Natural F-spin ordering (Fmax, Fmax ? 1, Fmax ? 2, ?, 0 or 1/2) is also observed with random interactions. Going beyond these, we also introduce pairing symmetry in the space defined by BEGOE(1+2)-F. Expectation values of the pairing Hamiltonian show that random interactions generate ground states with a maximum value for the expectation value for a given F and in these it is largest for F = Fmax = m/2.

Thermalization in one- plus two-body ensembles for dense interacting boson systems

Abstract Employing one- plus two-body random matrix ensembles for bosons, temperature and entropy are calculated, using different definitions, as a function of the two-body interaction strength λ for a system with 10 bosons ( m = 10 ) in five single-particle levels ( N = 5 ). It is found that in a region λ ∼ λ t , different definitions give essentially the same values for temperature and entropy, thus defining a thermalization region. Also, ( m , N ) dependence of λ t has been derived. It is seen that λ t is much larger than the λ values where level fluctuations change from Poisson to GOE and strength functions change from Breit–Wigner to Gaussian.

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

For bosons carrying spin-one degree of freedom, we introduce an embedded Gaussian orthogonal ensemble of random matrices generated by random two-body interactions in the presence of a mean field that is spin (S) scalar [called BEGOE(1+2)-S1]. Embedding algebra for the ensemble, for m bosons in Ω number of single-particle levels (each triply degenerate), is U(3Ω)⊃G⊃G1⊗SO(3) with SO(3) generating the spin S. A method for constructing the ensemble for a given (Ω,m,S) has been developed. Numerical calculations show that (i) the form of the fixed-(m, S) density of states is close to a Gaussian; (ii) for a strong enough interaction, level fluctuations follow GOE; (iii) fluctuation in energy centroids is large; and (iv) spectral widths are nearly constant with respect to S for S<S(max)/2. Moreover, we identify two different pairing symmetry algebras in the space defined by BEGOE(1+2)-S1 and numerical results show that random interactions generate ground states with maximal value for the pair expectation value.

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

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

Probability distribution of the ratio of consecutive level spacings in interacting particle systems

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Level-spacing statistics and spectral correlations in diffuse van der Waals clusters

. 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

Poisson to GOE transition in the distribution of the ratio of consecutive level spacings

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Transitions in eigenvalue and wavefunction structure in (1+2) -body random matrix ensembles with spin.

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 (

Strength functions for interacting bosons in a mean-field with random two-body interactions

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