Related papers: Chaitin's Omega and an Algorithmic Phase Transitio…
In this work, we present a compact analytical approximation for the quantum partition function of systems composed of quantum oscillators. The proposed formula is general and applicable to an arbitrary number of oscillators described by a…
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed by our former works [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008] and [K. Tadaki, Proceedings of…
Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One…
Number theory is considered, by proposing quantum mechanical models and string-like models at zero and finite temperatures, where the factorization of number into prime numbers is viewed as the decay of particle into elementary particles…
The critical properties of an infinitely long Ising strip with finite width L joined periodically or antiperiodically are investigated by analyzing the distribution of partition function zeros. For periodic boundary condition, the the…
We propose a relationship between thermodynamic phase transitions and ground-state quantum phase transitions in systems with variable Hamiltonian parameters. It is based on a link between zeros of the canonical partition function at complex…
At finite temperature, conserved charges undergo thermal fluctuations in a quantum many-body system in the grand canonical ensemble. The full structure of the fluctuations of the total U(1) charge $Q$ can be succinctly captured by the…
The interplay of quantum and thermal fluctuations in the vicinity of a quantum critical point characterizes the physics of strongly correlated systems. Here we investigate this interplay from a quantum information perspective presenting the…
We study the first-passage time (FPT) problem for widespread recurrent processes in confined though large systems and present a comprehensive framework for characterizing the FPT distribution over many time scales. We find that the FPT…
The unavoidable irreversible losses of power in a heat engine are found to be of quantum origin. Following thermodynamic tradition a model quantum heat engine operating by the Otto cycle is analyzed. The working medium of the model is…
We review the theoretical behaviour of the total and one-particle structure factors at a quantum phase transition for temperature T=0. The predictions are compared with exact or numerical results for the transverse Ising model, the…
We provide here an explicit example of Khinchin's idea that the validity of equilibrium statistical mechanics in high dimensional systems does not depend on the details of the dynamics. This point of view is supported by extensive numerical…
We compute higher order contributions to the free energy of noncommutative quantum electrodynamics at a nonzero temperature $T$. Our calculation includes up to three-loop contributions (fourth order in the coupling constant $e$). In the…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
Phase transitions which occur at zero temperature when some non-thermal parameter like pressure, chemical composition or magnetic field is changed are called quantum phase transitions. They are caused by quantum fluctuations which are a…
A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a non-zero value of the packing fraction. The zero-temperature constraint of force-balance plays a crucial role in…
A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…
In this article, we show that a quantum gas, a collection of massive, non-interacting, indistinguishable quantum particles can be realized as a thermodynamic machine as an artifact of energy quantization and hence bears no classical analog.…
With the help of quantum mechanics one can formulate a model of associative memory with optimal storage capacity. I generalize this model by introducing a parameter playing the role of an effective temperature. The corresponding…
We provide an exact expression of the moment of the partition function for random energy models of finite system size, generalizing an earlier expression for a grand canonical version of the discrete random energy model presented by the…