Related papers: Is there quantum chaos in the prime numbers?
The frequency of occurrence of prime numbers at unit number spacing intervals exhibits selfsimilar fractal fluctuations concomitant with inverse power law form for power spectrum generic to dynamical systems in nature such as fluid flows,…
Recent years have seen an increasing interest in quantum chaos and related aspects of spatially extended systems, such as spin chains. However, the results are strongly system dependent, generic approaches suggest the presence of many-body…
Recent studies have shown that there is a strong interplay between quantum complexity and quantum chaos. In this work, we consider a new method to study geometric complexity for interacting non-Gaussian quantum mechanical systems to…
Dynamical signatures of quantum chaos are observed in the survival probability of different initial states, in a system of cold atoms trapped in a linear chain with site noise and open boundary conditions. It is shown that chaos is present…
Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). It is shown that multiplicative nature of the noise is the main reason for the…
We study the interplay between regular and chaotic dynamics at the critical point of a generic first-order quantum phase transition in an interacting boson model of nuclei. A classical analysis reveals a distinct behavior of the coexisting…
We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states. We prove that the resulting…
A simple criterion is derived in order that a number sequence ${\cal S}_n$ is a permitted spectrum of a quantized system. The sequence of the prime numbers fulfils the criterion and the corresponding one-dimensional quantum potential is…
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the…
It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We compute numerically eigenvalues and eigenfunctions of the quantum Hamiltonian that describes the quantum mechanics of a point particle moving freely in a particular three-dimensional hyperbolic space of finite volume and investigate the…
How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical…
We present an overview of our studies on the nonequilibrium dynamics of quantum systems that have many interacting particles. Our emphasis is on systems that show strong level repulsion, referred to as chaotic systems. We discuss how full…
Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a…
[This is the unpublished supplemental information from 1989 to the paper: J.M. Deutsch, "Quantum statistical mechanics in a closed system." Phys. Rev. A, 43(4), 2046 (1991).] A closed quantum mechanical system does not necessarily give time…
The eigenvalue statistics of quantum ideal gases with single particle energies $e_n=n^\alpha$ are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the…
We check the eigenvalue spectrum of the $\Phi^{4}_{1+1}$ Hamiltonian against Poisson or Wigner behavior predicted from random matrix theory. We discuss random matrix theory as a tool to discriminate the validity of a model Hamiltonian…
The prime numbers have been a source of fascination for millenia and continue to surprise us. Motivated by the hyperuniformity concept, which has attracted recent attention in physics and materials science, we show that the prime numbers in…
Quantum statistics originate from the physics of state preparation. It is therefore wrong to think of quantum states as fundamental. In fact, quantum states are merely summaries of dynamical processes that randomize the properties of the…