Related papers: On the Quantum Density of States and Partitioning …
We study the density of quasiparticle states of dirty d-wave superconductors. We show the existence of singular corrections to the density of states due to quantum interference effects. We then argue that the density of states actually…
In the context of quantum information, highly nonlinear regimes, such as those supporting solitons, are marginally investigated. We miss general methods for quantum solitons, although they can act as entanglement generators or as…
We present an application of particle statistics to the problem of optimal ambiguous discrimination of quantum states. The states to be discriminated are encoded in the internal degrees of freedom of identical particles, and we use the…
The number partitioning problem consists of partitioning a sequence of positive numbers ${a_1,a_2,..., a_N}$ into two disjoint sets, ${\cal A}$ and ${\cal B}$, such that the absolute value of the difference of the sums of $a_j$ over the two…
For almost two decades, it has been believed that the quantum statistical properties of bosons are preserved in plasmonic systems. This idea has been stimulated by experimental work reporting the possibility of preserving nonclassical…
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into…
We study space-time resolved densities of particle-hole pairs produced by an external time-dependent field acting on non-interacting non-relativistic particles. It is shown that, at least in some cases, the densities are not affected by…
The quantum problem of four particles in $\mathbb{R}^d$ ($d\geq 3$), with arbitrary masses $m_1,m_2,m_3$ and $m_4$, interacting through an harmonic oscillator potential is considered. This model allows exact solvability and a critical…
We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different…
We provide a group-theoretical classification of the entangled states of N identical particles. The connection between quantum entanglement and the exchange symmetry of the states of N identical particles is made explicit using the duality…
It is well-known that a dilute one-dimensional (1D) gas of bosons with infinitely strong repulsive interactions behaves like a gas of free fermions. Just as with conduction electrons in metals, we consider a single-particle picture of the…
Quantum mechanics is considered to arise from an underlying classical structure (``hidden variable theory'', ``sub-quantum mechanics''), where quantum fluctuations follow from a physical noise mechanism. The stability of the hydrogen ground…
For a subset $\mathcal A\subset \mathbb N$, let $p_{\mathcal A}(n)$ denote the restricted partition function which counts partitions of $n$ with all parts lying in $\mathcal A$. In this paper, we use a variation of the Hardy-Littlewood…
The origin of the excess vibrational density of states (DOS) beyond Debye's theory in amorphous solids (often referred to as the Boson peak) has been attributed to the presence of quasi-localized vibrational modes in recent years. However,…
The very large transverse momenta and large multiplicities available in present LHC experiments on pp collisions allow a much closer look at the corresponding distributions. Some time ago we discussed a possible physical meaning of apparent…
The asymptotic form of the average probability to count $N$ indistinguishable identical particles in a small number $r \ll N$ of binned-together output ports of a $M$-port Haar-random unitary network, proposed recently in \textit{Scientific…
Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study Boson sampling from general,…
The local density of states (LDOS) in finite quantum wires is calculated as a function of discrete energies and position along the wire. By using a combination of numerical density matrix renormalization group (DMRG) calculations and…
The statistical problem of the distribution of $s$ quanta of equal energy $\epsilon_0$ and total energy $E$ among $N$ distinguishable particles is resolved using the conventional theory based on Boltzmann's principle of equal probabilities…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…