相关论文: Riemann zeta function and quantum chaos

The Riemann Hypothesis (RH), one of the most profound unsolved problems in mathematics, concerns the nontrivial zeros of the Riemann zeta function. Establishing connections between the RH and physical phenomena could offer new perspectives…

We study numerically the imperfection effects in the quantum computing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantum computation…

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.

We have dealt with the Euler's alternating series of the Riemann zeta function to define a regularized ratio appeared in the functional equation even in the critical strip and showed some evidence to indicate the hypothesis. We briefly…

We describe some highlights in the theory of chaos, that started with Poincare (1899). Generic systems have both ordered and chaotic domains. Chaos appears mainly near un- stable periodic orbits. Large chaotic domains are due to resonance…

New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…

Measurement quantum mechanics, the theory of a quantum system which undergoes a measurement process, is introduced by a loop of mathematical equivalencies connecting previously proposed approaches. The unique phenomenological parameter of…

Riemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of integrable model. We…

Quantum graphs are a paradigmatic model for quantum chaos as well as for spectral theory. We give a concise didactical introduction to quantum graphs, or Schr\"odinger Hamiltonians on metric graphs, with a focus on results related to…

Numerical investigations around a transformation of Landau's formula suggest certain statistical regularities in the distribution of zeros of the Riemann zeta function.

Physics is a fertile environment for trying to solve some number theory problems. In particular, several tentative of linking the zeros of the Riemann-zeta function with physical phenomena were reported. In this work, the Riemann operator…

Renormdynamic equations of motion and their solutions are given. New equation for NBD distribution and Riemann zeta function invented. Explicit forms of the z-Scaling functions are constructed.

The intrinsic multivaluedness of interaction process, revealed in Part I of this series of papers, is interpreted as the origin of the true dynamical (in particular, quantum) chaos. The latter is causally deduced as unceasing series of…

We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-1/2 lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what…

Here are a few random thoughts on the interpretations of the quantum double slit experiment, the Mach Zehnder experiment, the delayed-choice experiment and the measurement problem.

Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the…

We have recently suggested a quantum action, which has the form of a classical action and takes into account quantum effects via renormalized action parameters. Here we apply it to quantum chaos. We study a system in 2-D with weak…

This article examines the relationship between classical and quantum propagation of chaos. (In this context, "chaos" refers to the Boltzmann's Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation of chaos is shown…

This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the…

This note is a short survey of two topics: Archimedean zeta functions and Archimedean oscillatory integrals. We have tried to portray some of the history of the subject and some of its connections with similar devices in mathematics. We…