相关论文: Riemann zeta function and quantum chaos

By some hypergeometric summation theorems, the authors establish a series of new infinite summation formulas involving generalized harmonic numbers related to Riemann-Zeta function, with three different patterns.

We introduce a screw function corresponding to the Riemann zeta-function and study its properties from various aspects. Typical results are several equivalent conditions for the Riemann hypothesis in terms of the screw function. One of them…

We show that Hurwitz numbers may be generated by certain correlation functions which appear in quantum chaos.

A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily…

The main subject to study in this paper are properties of the sequence of reversely iterated segments. Especially, we will examine properties of chaotic behavior of the sequence of measures of corresponding segments. Our results are not…

We examine published arguments which suggest that the Riemann Hypothesis may not be true. In each case we provide evidence to explain why the claimed argument does not provide a good reason to doubt the Riemann Hypothesis. The evidence we…

We present a new expansion of the zeta-function of Riemann. The current formalism -- which combines both the idea of interpolation with constraints and the concept of hypergeometric functions -- can, in a natural way, be generalised within…

We review the dissipative quantum model of brain and present recent developments related with the r\^ole of entanglement, quantum noise and chaos in the model.

We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating…

An assessment of the present status of the theory, some immediate tasks which are suggested thereby and some questions whose answers may require a longer breath since they relate to significant changes in the conceptual and mathematical…

Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it…

A short critical review of the concept of decoherence, its consequences, and its possible implications for the interpretation of quantum theory is given.

We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$.

A variant for the Hilbert and Polya spectral interpretation of the Riemann zeta function is proposed. Instead of looking for a self-adjoint linear operator H, whose spectrum coincides with the Riemann zeta zeros, we look for the complex…

We provide a rather extended introduction to the group field theory approach to quantum gravity, and the main ideas behind it. We present in some detail the GFT quantization of 3d Riemannian gravity, and discuss briefly the current status…

The Renormalization group in field theories happens to resemble dynamical systems in many ways. In this paper, we discuss the unexpected connection between chaos and duality in field theories. In a sense, that various dual field theories…

This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…

One of the most famous problems in mathematics is the Riemann hypothesis: that the non-trivial zeros of the Riemann zeta function lie on a line in the complex plane. One way to prove the hypothesis would be to identify the zeros as…

A review of some recent results and ideas about the expected behaviour of large chaotic systems and fluids.

The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be…