相关论文: Polynomial method for canonical calculations

We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can only be applied to small systems. By contrast, we demonstrate that quantum…

We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…

We present a self-contained theory for the exact calculation of particle number counting statistics of non-interacting indistinguishable particles in the canonical ensemble. This general framework introduces the concept of auxiliary…

A general formula for the grand canonical partition function for a para Fermi system of any order and of any number of levels is derived.

The partition function for a system of non-interacting $N-$particles can be found by summing over all the states of the system. The classical partition function for an ideal gas differs from Bosonic or Fermionic partition function in the…

It is demonstrated that the canonical distribution for a subsystem of a closed system follows directly from the solution of the time-reversible Newtonian equation of motion in which the total energy is strictly conserved. It is shown that…

In this paper, we formulate statistical mechanics of the polymerized systems in the semiclassical regime. On the corresponding polymeric symplectic manifold, we set up a noncanonical coordinate system in which all of the polymeric effects…

We describe a method to compute thermodynamic quantities in the harmonic approximation for identical bosons and fermions in an external confining field. We use the canonical partition function where only energies and their degeneracies…

We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not…

A general formula for the canonical partition function for a system obeying any statistics based on the permutation group is derived. The formula expresses the canonical partition function in terms of sums of Schur functions. The only…

A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…

We derive a new formulation to calculate the excess chemical potential of a fraction of $N_1$ particles interacting with $N_2$ particles of a different species. The excess chemical potential is calculated numerically from first principles…

A new approach to describe comminution processes in general ball mills as a macroscopic canonical ensemble is proposed. Using hamiltonian method, the model is able to take simultaneously into account the internal dynamics from mechanical…

The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…

The method for calculation of the canonical decomposition that approximates a tensor of high order is considered, which requires moderate computational resources. It is based on the replacement of the approximation error norm (global…

In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the…

The exact canonical partition function of a hard disk system in a narrow quasi-one dimensional pore of given length and width is derived analytically in the thermodynamic limit. As a result the many body problem is reduced to solving two…

We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…

The partition function of composite bosons ("cobosons" for short) is calculated in the canonical ensemble, with the Pauli exclusion principle between their fermionic components included in an exact way through the finite temperature…