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The strong confinement of semiconductor excitons in a quantum dot gives rise to atom-like behavior. The full benefit of such a structure is best observed in resonant excitation where the excited state can be deterministically populated and…
We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically…
Elementary particle detectors fall broadly into only two classes: phase-transformation devices, such as the bubble chamber, and charge-transfer devices like the Geiger-Mueller tube. Quantum measurements are seen to involve transitions from…
The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime is studied as a function of the separation $d$ between the electron and valence hole layers. The abrupt change in the…
We show that the symplectic and orthogonal character analogues of Okounkov's Schur measure (on integer partitions) are determinantal, with explicit correlation kernels. We apply this to prove certain Borodin-Okounkov-Gessel-type results…
We report on the study of the fractional quantum Hall effect at the filling factor 5/2 using exact diagonalization method with torus geometry. The particle-hole symmetry breaking effect is considered using an additional three-body…
Dissociative electron attachment (DEA) is one of the processes that shows a strong coupling between the nuclear and electronic degrees of freedom in a molecule. This coupling results in an efficient transformation of the kinetic energy of…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
A determinant in algebraic $K$-theory is associated to any two almost commuting Fredholm operators. On the other hand, one can calculate a homologically defined invariant known as joint torsion. We answer in the affirmative a conjecture of…
We discuss various aspects of positive kernel method of quantization of the one-parameter groups $\tau_t \in \mbox{Aut}(P,\vartheta)$ of automorphisms of a $G$-principal bundle $P(G,\pi,M)$ with a fixed connection form $\vartheta$ on its…
A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time…
Let $X$ be a mean zero Gaussian random vector in a separable Hilbert space ${\mathbb H}$ with covariance operator $\Sigma:={\mathbb E}(X\otimes X).$ Let $\Sigma=\sum_{r\geq 1}\mu_r P_r$ be the spectral decomposition of $\Sigma$ with…
A derivation operator and a divergence operator are defined on the algebra of bounded operators on the symmetric Fock space over the complexification of a real Hilbert space $\eufrak{h}$ and it is shown that they satisfy similar properties…
As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…
Determinantal process is a dynamical extension of a determinantal point process such that any spatio-temporal correlation function is given by a determinant specified by a single continuous function called the correlation kernel.…
This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming…
A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…
We report on the study of many-body interactions in a single high quality V-shaped quantum wire by means of continuous and time-resolved microphotoluminescence. The transition from a weakly interacting exciton gas when the carrier density n…
We present a fast and accurate algorithm for the evaluation of nonlocal (long-range) Coulomb and dipole-dipole interactions in free space. The governing potential is simply the convolution of an interaction kernel $U(\bx)$ and a density…
Binary collisions in Fermi systems obey two fundamental symmetries corresponding to the space and time inversion and to the interchange of particles and holes. We show that beyond the local and instant approximation of scattering-in and…