Related papers: Eigenvalue statistics in quantum ideal gases
We calculate certain features of Bose-Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are…
The question of how classical thermodynamic laws emerge from the underlying quantum substrate lies at the foundations of physics. Here, we examine the validity of the ideal gas law (IGL) for a single quantum particle confined within a…
The statistics of $q$-oscillators, quons and to some extent, of anyons are studied and the basic differences among these objects are pointed out. In particular, the statistical distributions for different bosonic and fermionic…
Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional…
The fundamental constants of electromagnetism, gravity and quantum mechanics can be related empirically by the numerical approximation $\ln(V_e/V_P)\approx \alpha^{-1}$, where $\alpha$ is the low energy value of the electromagnetic fine…
In this work we study the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
In a quantum system, different energy eigenstates have different properties or features, allowing us define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstates in an energy shell…
Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct…
In this work, improvements are introduced to the current models of the ideal Fermi gas and the ideal Bose gas by incorporating the quantum nature of phase space, which is directly linked to the uncertainty principle. These improved models…
A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an uncertainity may be either an intrinsic property of a particle or can be viewed as an…
The statistical mechanics of quarks and gluons are investigated within the context of the canonical ensemble. Recursive techniques are developed which enforce the exact conservation of baryon number, total isospin, electric charge,…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
We propose an experimental scheme to probe the quantum statistics of two identical particles. The transition between the quantum and classical statistics of two identical particles is described by the particles having identical multiple…
Analysis of edge-state energies in the integer quantum Hall effect is carried out within the semiclassical approximation. When the system is wide so that each edge can be considered separatly, this problem is equivalent to that of a one…
In this work we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. As before we utilize the methods, properties, and results obtained by means of classical…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
A quantum statistical system with energy dissipation is studied. Its statisitics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble. The eigenenergies are shown to form stable structure in…
A quantum statistical random system with energy dissipation is studied. Its statistics is governed by random complex-valued non-Hermitean Hamiltonians belonging to complex Ginibre ensemble of random matrices. The eigenenergies of…