Universal spectral correlations in ensembles of random normal matrices

Prakash, Ravi; Pandey, Akhilesh

doi:10.1209/0295-5075/110/30001

Cited by 5 publications

(6 citation statements)

References 36 publications

(116 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The eigenvalues starts falling towards center and constitute a ring like structure. We have studied the time reversal broken (γ = 0) case for this system in [20].…”

Section: Dissipative Quantum Kicked Rotormentioning

confidence: 99%

“…The time reversal preserved case corresponds to γ = 0. We construct the spectra using (20) with γ = 0 and N = 501. The spectral density is not uniform in this case as shown in Fig.…”

Section: Dissipative Quantum Kicked Rotormentioning

confidence: 99%

“…The imaginary part of the eigenvalues and the eigenangles are considered as a manifestation of dissipation in the system. The spacing distribution for the Ginibre ensemble shows cubic repulsion in the eigenvalues [38] and is verified in Dissipative Quantum Kicked Rotor (DQKR) without TRI [27,[38][39][40][41].…”

mentioning

confidence: 98%

“…It may be noted that this letter is concerned with β = 1, 2 and we show the spacing distribution for β = 4 for completeness. There exist systems where spectral density may not be uniform [39] and one requires the unfolding method to remove the global variations. In order to unfold the spectra of such cases, we scale each spacing, s, by √ πR 1 to get the spectral density similar to that of the Ginibre ensemble, where R 1 is the average spectral density around the eigenvalue pair.…”

mentioning

confidence: 99%

“…Since, the Floquet operator F is no longer unitary, the eigenvalues start falling towards the center and constitute a ring-like structure. We have studied the time-reversal broken (γ = 0) case for this system in [39]. The time-reversal preserved case corresponds to γ = 0.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Universality classes of quantum chaotic dissipative systems

Jaiswal¹,

Pandey²,

Prakash³

2019

EPL

Self Cite

View full text Add to dashboard Cite

We study the ensemble of complex symmetric matrices. The ensemble is useful in the study of effect of dissipation on systems with time reversal invariance. We consider the nearest neighbor spacing distribution and spacing ratio to investigate the fluctuation statistics and show that these statistics are similar to that of dissipative chaotic systems with time reversal invariance. We show that, unlike cubic repulsion in eigenvalues of Ginibre matrices, these ensemble exhibits a weaker repulsion. The nearest neighbor spacing distribution exhibits P (s) ∝ −s 3 log s for small spacings. We verify our results for quantum kicked rotor with time reversal invariance. We show that the rotor exhibits similar spacing distribution in dissipative regime. We also discuss a random matrix model for transition from time reversal invariant to broken case.

show abstract

“…The eigenvalues starts falling towards center and constitute a ring like structure. We have studied the time reversal broken (γ = 0) case for this system in [20].…”

Section: Dissipative Quantum Kicked Rotormentioning

confidence: 99%

“…The time reversal preserved case corresponds to γ = 0. We construct the spectra using (20) with γ = 0 and N = 501. The spectral density is not uniform in this case as shown in Fig.…”

Section: Dissipative Quantum Kicked Rotormentioning

confidence: 99%

mentioning

confidence: 98%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Universality classes of quantum chaotic dissipative systems

Jaiswal¹,

Pandey²,

Prakash³

2019

EPL

Self Cite

View full text Add to dashboard Cite

show abstract

A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary Ensemble

Choudhury

Mukherjee

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two point Out of Time Order Correlation function (OTOC) expressed in terms of square of the commutator bracket of quantum operators which are separated in time. We also provide a strict model independent bound on the measure of quantum chaos, −1/N (1 − 1/π) ≤ SFF ≤ 0 and 0 ≤ SFF ≤ 1/πN , valid for thermal systems with large and small number of degrees of freedom respectively. Based on the appropriate physical arguments we give a precise mathematical derivation to establish this alternative strict bound of quantum chaos.Quantum description of chaos has three important properties boundedness, exponential sensitivity and infinite recurrence. In the context of dynamical systems the concept of quantum chaos describes quantum signatures of classically chaotic systems. Quantum chaos can be formulated for two observable represented by hermitian operators X(t) and Y (t) using their commutator relation. This actually explains the perturbation effect of one operator Y (t) on the measurement of other operator X(t). Strength of this perturbation can be measured formulating a function:(1) at temperature β = 1/T , also Z is the partition function of the system and H representing the system Hamiltonian. Here we assume that X and Y have zero one point function. Hence we use two point function for measuring quantum chaos, which technically has been explained by the late time behavior of the function C(t) from which we can get a bound on quantum chaos. It has been previously shown that due to quantum effects two point function for chaos decrease to a particular constant value. This decrease rate has an exponential growth with a factor λ L (Lyapunov Exponent) which entirely depends on system properties and observable. Thus a bound on Lyapunov Exponent can be treated as measure of quantum chaos. Using quantum field theory it has been shown that an universal bound [1] on the Lyapunov exponent exists:This bound is unique feature for all classes of out of equilibrium quantum field theory set up. We have also discussed the saturation of chaos bound at late time scale using Random matrix theory (RMT) which was previously discussed in the quantization of classical chaotic systems, usually in the semi-classical or high quantumnumber regimes. For this discussion we construct Spectral From Factor (SFF) [2], which is arising from two point out of time orderd correlation (OTOC) function in RMT has been used to derive an alternative but strong bound on chaos. This gives us extra freedom to generalize our discussion for any quantum system with random interaction. This interaction has been included by a polynomial potential function of general order. Discussing the late time behavior of SFF. we get its upper bound. Also this approach is unique as the bound is valid for any arbitrary (infinite and finite) temperature. We also obtained a lower bound for SFF which depicts t...

show abstract

Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at nonintegerβ

2022

View full text Add to dashboard Cite

A random matrix representation is proposed for the two-dimensional (2D) Coulomb gas at inverse temperature β. For 2 × 2 matrices with Gaussian distribution we analytically compute the nearest-neighbor spacing distribution of complex eigenvalues in radial distance. Because it does not provide such a good approximation as the Wigner surmise in 1D, we introduce an effective β eff (β ) in our analytic formula that describes the spacing obtained numerically from the 2D Coulomb gas well for small values of β. It reproduces the 2D Poisson distribution at β = 0 exactly, that is valid for a large particle number. The surmise is used to fit data in two examples, from open quantum spin chains and ecology. The spacing distributions of complex symmetric and complex quaternion self-dual ensembles of non-Hermitian random matrices, that are only known numerically, are very well fitted by noninteger values β = 1.4 and β = 2.6 from a 2D Coulomb gas, respectively. These two ensembles have been suggested as the only two symmetry classes, where the 2D bulk statistics is different from the Ginibre ensemble.

show abstract

Universal spectral correlations in ensembles of random normal matrices

Cited by 5 publications

References 36 publications

Universality classes of quantum chaotic dissipative systems

Universality classes of quantum chaotic dissipative systems

A bound on quantum chaos from Random Matrix Theory with Gaussian Unitary Ensemble

Spacing distribution in the two-dimensional Coulomb gas: Surmise and symmetry classes of non-Hermitian random matrices at nonintegerβ

Contact Info

Product

Resources

About