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In this review we describe statistical mechanics of quantum systems in the presence of a Killing horizon and compare statistical-mechanical and one-loop contributions to black hole entropy. Studying these questions was motivated by attempts…

We generalize Page's result on the entanglement entropy of random pure states to the many-body eigenstates of realistic disordered many-body systems subject to long range interactions. This extension leads to two principal conclusions:…

This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…

We study the quantification of coherence in infinite dimensional systems, especially the infinite dimensional bosonic systems in Fock space. We show that given the energy constraints, the relative entropy of coherence serves as a…

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbour interactions. We focus on the DE of a subsystem of L continuous spins. We show…

The finiteness of black hole entropy suggest that spacetime is fundamentally discrete, and hints at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should…

The threshold behaviour of the K-Satisfiability problem is studied in the framework of the statistical mechanics of random diluted systems. We find that at the transition the entropy is finite and hence that the transition itself is due to…

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…

We consider the contribution to the entropy from fields in the background of a curved time-independent metric. To account for the curvature of space, we postulate a position-dependent UV cutoff. We argue that a UV cutoff on energy naturally…

We characterize symmetric spaces without focal points by the equality case of general equalities between geometric quantities.

Concepts of quantum open systems and ideas of correlation dynamics in nonequilibrium statistical mechanics, as well as methods of closed-time-path effective action and influence functional in quantum field theory can be usefully applied for…

Measure-theoretic and topological entropy are classical invariants in the theory of dynamical systems. There are several recently developed entropy type invariants for systems of sub-exponential growth: sequence entropy, slow entropy,…

Stabilizer entropies (SE) measure deviations from stabilizer resources and as such are a fundamental ingredient for quantum advantage. In particular, the interplay of SE and entanglement is at the root of the complexity of classically…

This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected chord diagrams is further studied and new…

An intriguing question related to black hole thermodynamics is that the entropy of a region shall scale as the area rather than the volume. In this essay we propose that the microscopical degrees of freedom contained in a given region of…

The topological entropy dimension is mainly used to distinguish the zero topological entropy systems. Two types of topological entropy dimensions, the classical entropy dimension and the Pesin entropy dimension, are investigated for…

The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization…

We analyze how measured quantum dynamical systems store and process information, introducing sofic quantum dynamical systems. Using recently introduced information-theoretic measures for quantum processes, we quantify their information…

Open quantum systems interact with their environment and their dynamical behaviour depends strongly both on the spectral properties of the environment and the structure of the interaction between the physical system and the environment. We…

Control over the quantum dynamics of chaotic kicked rotor systems is demonstrated. Specifically, control over a number of quantum coherent phenomena is achieved by a simple modification of the kicking field. These include the enhancement of…