Related papers: Riemann zeta function and quantum chaos
The temporal behavior of quantum mechanical systems is reviewed. We study the so-called quantum Zeno effect, that arises from the quadratic short-time behavior, and the analytic properties of the ``survival" amplitude. It is shown that the…
The properties of a fictitious, fermionic, many-body system based on the complex zeros of the Riemann zeta function are studied. The imaginary part of the zeros are interpreted as mean-field single-particle energies, and one fills them up…
The concept of structural invariance previously introduced by the authors is used to argue that the connection between random matrix theory and quantum systems with a chaotic classical counterpart is in fact largely exact in the…
The behavior displayed by a quantum system when it is perturbed by a series of von Neumann measurements along time is analyzed. Because of the similarity between this general process with giving a deck of playing cards a shuffle, here it is…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
There are many striking phenomena which are attributed to ``quantum coherence''. It is natural to wonder if there are new quantum coherence effects waiting to be discovered which could lead to interesting results and perhaps even practical…
A $q$-analogue of the Hurwitz zeta-function is introduced through considerations on the spectral zeta-function of quantum group $SU_{q}(2)$, and its analytic aspects are studied via the Euler-MacLaurin summation formula. Asymptotic formulas…
We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period doubling…
Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those…
We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…
The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of…
On place quelques applications r\'ecentes de la th\'eorie du Chaos en perspective avec la th\'eorie classique de Boltzmann.
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
Extensive coherent control over quantum chaotic diffusion using the kicked rotor model is demonstrated and its origin in deviations from random matrix theory is identified. Further, the extent of control in the presence of external…
We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov…
We discuss Shnirelman's Quantum Ergodicity Theorem, giving an outline of a proof and an overview of some of the recent developments in mathematical Quantum Chaos.
A proof for the original Riemann hypothesis is proposed based on the infinite Hadamard product representation for the Riemann zeta function and later generalized to Dirichlet L-functions. The extension of the hypothesis to other functions…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
The main idea of "Quantum Chaos" studies is that Quantum Mechanics introduces two energy scales into the study of chaotic systems: One is obviously the mean level spacing $\Delta\propto\hbar^d$, where $d$ is the dimensionality; The other is…
This study addresses a longstanding question regarding the mathematical proof of chaotic behavior in kinetic differential equations. Following the numerous numerical and experimental results in the past 50 years, we introduce two formal…