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The single-particle density is the most basic quantity that can be calculated from a given many-body wave function. It provides the probability to find a particle at a given position when the average over many realizations of an experiment…
State-space systems encompass a broad class of algorithms used for modeling and forecasting time series. For such systems to be effective, two objectives must be met: (i) accurate point forecasts of the time series must be produced, and…
The paper demonstrates that the canonical probability distribution of the occupancy numbers of a bosonic system is multinomial, and shows how the thermodynamics of the canonical system descends from this distribution. The categorical…
We present a systematic approach to construct complete equations of state (EOSs), or to ensure thermodynamic consistency of complete and incomplete forms of EOSs using a minimal and sufficient set of relations. We apply the proposed…
By use of the conservation laws a four-site Hubbard model coupled to a particle bath within an external magnetic field in z-direction was diagonalized. The analytical dependence of both the eigenvalues and the eigenstates on the interaction…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
We propose a method to calculate finite-temperature properties of a quantum many-body system for a microcanonical ensemble by introducing a pure quantum state named here an energy-filtered random-phase state, which is also a potentially…
We investigate, how finite temperature influences quantum coherence in multipartite open systems by analyzing a tripartite spin boson model subjected to non-Markovian dephasing. Two distinct environmental configurations are considered viz.…
We prove the existence of correlations between the equilibrium states at different temperatures of the multi-$p$-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models.…
We show how the macroscopic state variables pressure, entropy and temperature of equilibrium thermodynamics can be consistently derived from the (quantum) chaotic spectral structure of one or two particles in two-dimensional domains. This…
In a system of N particles, with continuous size polydispersity there exists N(N-1) number of partial structure factors making it analytically less tractable. A common practice is to treat the system as an effective one component system…
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and…
By detailed Molecular Dynamics and Monte Carlo simulations %of a realistic model we show that granular materials at rest can be described as thermodynamics systems. First we show that granular packs can be characterized by few parameters,…
Quantitative description of finite-temperature properties of displacive ferroelectrics, and in particular the critical behavior, is of fundamental importance to both theory and device design, going beyond the Landau-Ginzburg approach, which…
In alloy thermodynamics, stochastically disordered state (SDS), where each lattice point is stochastically occupied by constituents according to given composition, is typically referred to investigating physical properties for homogeneously…
Predictive state representation~(PSR) uses a vector of action-observation sequence to represent the system dynamics and subsequently predicts the probability of future events. It is a concise knowledge representation that is well studied in…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
The configurational density of states (CDOS) encodes all the relevant thermodynamic information contained in the interaction potentials for statistical mechanical systems. However, its explicit computation is usually a challenge for…
We have considered a model of a small finite system with internal particles and surface degrees of freedom. All the main statistical distributions were explicitly obtained, on a pre thermodynamic limit basis. The concept of temperature or…
The thermodynamics for a system with given temperature, density, and volume is described by the Canonical ensemble. The thermodynamics for a corresponding system with the same temperature, volume, and average density is described by the…