Related papers: Off-Diagonal Series Expansion for Quantum Partitio…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
In this work, we propose a method for calculating the free energy of anisotropic quantum spin systems. We use the Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in…
Fixing the number of particles $N$, the quantum canonical ensemble imposes a constraint on the occupation numbers of single-particle states. The constraint particularly hampers the systematic calculation of the partition function and any…
Fractional derivative can be defined as a fractional power of derivative. The commutator (i/h)[H, ], which is used in the Heisenberg equation, is a derivation on a set of observables. A derivation is a map that satisfies the Leibnitz rule.…
There are problems with defining the thermodynamic limit of systems with long-range interactions; as a result, the thermodynamic behavior of these types of systems is anomalous. In the present work, we review some concepts from both…
Effects of Lie type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the…
A formulation of quantum mechanics is introduced based on a $2D$-dimensional phase-space wave function $\text{\reflectbox{\text{p}}}\mkern-3mu\text{p}\left(q,p\right)$ which might be computed from the position-space wave function…
A quark-magnetic Ginzburg-Landau (qHGL) gradient expansion of the free energy of two-flavor inhomogeneous quark matter in a magnetic field $H$ is derived analytically. It can be applied away from the Lifshitz point, generalizing standard…
Thermalization is investigated for the one-dimensional anisotropic antiferromagnetic Heisenberg model with dimerized nearest-neighbor interactions that break integrability. For this purpose the time evolution of local operator expectation…
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful…
We have done a study of the zero-dimensional $\lambda\phi^{4}$ model. Firstly, we exhibit the partition function as a simple exact expression in terms of the Macdonald's function for $Re(\lambda)>0$. Secondly, an analytic continuation of…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…
We discuss the prospects of performing high-order perturbative calculations in systems characterized by a vanishing temperature but finite density. In particular, we show that the determination of generic Feynman integrals containing…
We develop a quantum model based on the correspondence between energy distribution between harmonic oscillators and the partition of an integer number. A proper choice of the interaction Hamiltonian acting within this manifold of states…
This work establishes a connection between canonical perturbation series in quantum mechanics and a Kato expansion for the resolvent of the Liouville superoperator. Our approach leads to an explicit expression for a generator of a…
We calculate the partition function for "composite particles". For any finite number of states d, and in the following two cases: 1)all states have the same energy, 2)the energy is linearly distributed over the states, we transform the…
We model the dynamics of a closed quantum system brought out of mechanical equilibrium, undergoing a non-driven, spontaneous, thermodynamic transformation. In particular, we consider a quantum particle in a box with a moving and insulating…
Borel summable semiclassical expansions in 1D quantum mechanics are considered. These are the Borel summable expansions of fundamental solutions and of quantities constructed with their help. An expansion, called topological,is constructed…
In this article, we investigate the thermal properties of non-relativistic many-body systems at finite temperature and chemical potential. We compute the one-point function of various operators constructed out of the basic fields in ideal…