Multiparticle Wave Functions Research Articles

Exchange interaction for Mn acceptors in GaAs: Revealing its strong deformation dependence

In this paper we calculate exchange interaction constant between manganese ion inner electronic $d$-shell and GaAs valence band bounded hole using their microscopic multiparticle wave functions. We reveal its parametric dependence on crystal lattice deformations and find out that it could be about and even more than dozens percent when the strain tensor reaches values of $10^{-3} \div 10^{-2}$. This fact is in accordance with the previous hypothesis of deformation dependence of Mn acceptors in GaAs fine energy structure obtained from Raman spectroscopy, and we show that this dependence has the same magnitude. Also, we resolve here the problem of a substantial high temperature mismatch between well-developed theory and experimental data for the static magnetic susceptibility of Mn ions in GaAs. We show by numerical estimates and calculations that quite a strong parametric dependence of the exchange coupling value on GaAs lattice expansion determines the high temperature (above $50~$K) magnetic susceptibility reduction as well.

Multi-time dynamics of the Dirac-Fock-Podolsky model of QED

Dirac, Fock, and Podolsky devised a relativistic model in 1932 in which a fixed number of N Dirac electrons interact through a second-quantized electromagnetic field. It is formulated with the help of a multitime wave function ψ(t1,x1,…,tN,xN) that generalizes the Schrödinger multiparticle wave function to allow for a manifestly relativistic formulation of wave mechanics. The dynamics is given in terms of N evolution equations that have to be solved simultaneously. Integrability imposes a rather strict constraint on the possible forms of interaction between the N particles and makes the rigorous construction of interacting dynamics a long-standing problem, also present in the modern formulation of quantum field theory. For a simplified version of the multitime model, in our case describing N Dirac electrons that interact through a relativistic scalar field, we prove well-posedness of the corresponding multitime initial value problem and discuss the mechanism and type of interaction between the charges. For the sake of mathematical rigor, we are forced to employ an ultraviolet cutoff in the scalar field. Although this again breaks the desired relativistic invariance, this violation occurs only on the arbitrarily small but finite length-scale of this cutoff. In view of recent progress in this field, the main mathematical challenges faced in this work are, on the one hand, the unboundedness from below of the free Dirac Hamiltonians and the unbounded, time-dependent interaction terms, and on the other hand, the necessity of pointwise control of the multitime wave function.

Grand Canonical Ensembles, Multiparticle Wave Functions, Scattering Data, and Lattice Field Theories.

We show that information about scattering data of a quantum field theory can be obtained from studying the system at finite density and low temperatures. In particular we consider models formulated on the lattice that can be exactly dualized to theories of conserved charge fluxes on lattice links. Apart from eliminating the complex action problem at nonzero chemical potential μ, these dualizations allow for a particle world line interpretation of the dual fluxes from which one can extract data about the two-particle wave function. As an example we perform dual MonteCarlo simulations of the two-dimensional O(3) model at nonzero μ and finite volume, whose nonperturbative spectrum consists of a massive triplet of particles. At nonzero μ particles are induced in the system, which at sufficiently low temperature give rise to sectors of fixed particle number. We show that the scattering phase shifts can be obtained either from the critical chemical potential values separating the sectors or directly from the wave function in the two-particle sector. We find that both methods give excellent agreement with the exact result. We discuss the applicability and generality of the new approaches.

Brink model with tetrahedral alpha-particle clusters for three-particle forces

Three-particle interaction is introduced in the Brink model modification that takes into account an arbitrary localization of nucleons within alpha-particle clusters. Simultaneously, the class of single-particle variational functions is substantially extended by replacing the traditionally employed Gaussian function by the sum of Gaussian functions. In the case of the Bonche-Koonin-Negele (BKN) interaction, three Gaussian functions provide a good upper bound on the results of solving the Hartree-Fock equation for the 4He nucleus. It is shown that the BKN three-particle interaction simulates to some extent the effect of short-range correlations in the multiparticle wave function.

Polariton pendulum

A macroscopic quantum pendulum has now been created by confining a polariton condensate in a parabolic optical trap. Spectacular images of multiparticle wavefunctions are obtained by purely optical means.

Simulating strongly correlated multiparticle systems in a truncated Hilbert space

Representing a strongly interacting multi-particle wave function in a finite product basis leads to errors. Simple rescaling of the contact interaction can preserve the low-lying energy spectrum and long-wavelength structure of wave functions in one-dimensional systems and thus correct for the basis set truncation error. The analytic form of the rescaling is found for a two-particle system where the rescaling is exact. Detailed comparison between finite Hilbert space calculations and exact results for up to 5 particles show that rescaling can significantly improve the accuracy of numerical calculations in various external potentials. In addition to ground state energies, the low-lying excitation spectrum, density profile and correlation functions are studied. The results give a promising outlook for numerical simulations of trapped ultracold atoms.

Quantum counting algorithm and its application in mesoscopic physics

We present a quantum algorithm to transform the cardinality of a set of charged particles flowing along a quantum wire into a binary number. The setup performing this task (for at most N particles) involves log_2 N quantum bits serving as counters and a sequential read out. Applications include a divisibility check to experimentally test the size of a finite train of particles in a quantum wire with a one-shot measurement and a scheme allowing to entangle multi-particle wave functions and generating Bell states, Greenberger-Horne-Zeilinger states, or Dicke states in a Mach-Zehnder interferometer.

Quantum optics in waveguides with resonant atoms: Multi-photon scattering

Quantum scattering of photons inside a one-dimensional waveguide caused by a number of closely located resonant two-level atoms is studied using the theory of integrable quantum systems. The multi-particle wave function of scattered photons is represented as a sum of terms of different degrees of “entanglement.” For two-photon scattering we discuss explicitly differences in photon correlations for the single two-level atom case and the case of several atoms.

Preliminary results on approximating a wavefunction as an unconstrained sum of Slater determinants

AbstractA multiparticle wavefunction, which is a solution of the multiparticle Schrödinger equation, satisfies the antisymmetry condition, thus making it natural to approximate it as a sum of Slater determinants. Many current methods do so but, in addition, they impose structural constraints on the Slater determinants, such as orthogonality between orbitals or a particular excitation pattern. By removing these constraints, we hope to obtain much more efficient expansions.We use an integral formulation of the problem, a Green's function iteration, and a fitting procedure based on the computational paradigm of separated representations. For constructing and solving a matrix‐integral system of equations derived from antisymmetric inner products, we develop new algorithms with computational complexity competitive with current methods.We describe preliminary numerical results and make some observations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Bogoliubov theory of a Bose-Einstein condensate in the particle representation

In the number-conserving Bogoliubov theory of BEC the Bogoliubov transformation between quasiparticles and particles is nonlinear. We invert this nonlinear transformation and give general expression for eigenstates of the Bogoliubov Hamiltonian in particle representation. The particle representation unveils structure of a condensate multiparticle wavefunction. We give several examples to illustrate the general formalism.

Quantum groups and non-Abelian braiding in quantum Hall systems

Wave functions describing quasiholes and electrons in non-Abelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure underlying the braiding properties of these conformal blocks. We treat the electrons and the quasihole excitations as localised particles carrying charges related to a quantum group that is determined explicitly for the cases of interest. The quantum group description naturally allows one to analyse the braid group representations carried by the multi-particle wave functions. As an application, we construct the non-Abelian braid group representations which govern the exchange of quasiholes in the fractional quantum Hall effect states that have been proposed by N. Read and E. Rezayi [Phys. Rev. B 59 (1999) 8084], recovering the results of C. Nayak and F. Wilczek [Nucl. Phys. B 479 (1996) 529] for the Pfaffian state as a special case.

Quantum coins, dice, and children: Probability and quantum statistics

We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized that, even in the absence of interactions, (anti)symmetrizations of multiparticle wave functions destroy statistical independences and often lead to dramatic departures from our intuitive expectations.

On the Generalized Statistics Through the Deformation of the Exterior Algebra

Using a consistent deformation of the exterior algebra, we propose a generalized statistic depending on the Braid operator allowing this deformation. The deformed Fock space is constructed and the structure of multiparticle wave functions is given.

Precision Tests Find No Violation of Bose Statistics

The symmetrization postulate of quantum mechanics asserts that the multiparticle wavefunction for any collection of identical particles must be either wholly symmetric or wholly antisymmetric under the exchange of labels between any two particles. In nonrelativistic quantum mechanics, this postulate is a somewhat ad hoc assumption tacked onto the theory; wholly symmetric or antisymmetric wave functions are not the only ways of preserving the indistinguishability of identical particles.

Quantum mechanics on a space-time lattice using path integrals in a minkowski metric

A simple model of many-body quantum mechanics governed by completely local interactions in ordinary three-dimensional space is presented. The equations of motion, involving no Euclideanization of time, are elementary extensions of those describing random walks on a square lattice, and are far simpler than those obtained through standard path-integral theory. A quantity is defined in terms of populations of particles on the lattice, whose expectation value is proportional to the square of the multiparticle wave functions associated with the system; for sufficiently microscopic measurement scales, this generalized ‘density’ may take on negative values, thereby circumventing the constraints imposed by Bell's inequality.

Wave functions for continuum states of charged fragments.

Briggs's representation [Phys. Rev. A 41, 539 (1990)] of the Moller wave operator for multiparticle wave functions is applied to charged fragments using a limiting procedure to correctly account for the slow decrease of Coulomb interactions with distance. Approximate wave functions used to model ([ital e],2[ital e]) angular correlation measurments are obtained. Computed and measured angular correlations are compared to clarify the region of applicability of two approximations.

Three-dimensional generalization of anyon superconductivity.

A three-dimensional generalization of the wave function of Girvin et al. is constructed by taking the N\ensuremath{\rightarrow}\ensuremath{\infty} limit of a solution of the two-dimensional massless Dirac equation with an SU(N) gauge field. The resulting wave function is closely related to instanton solutions of the self-dual Einstein quations, and can be used to construct a multiparticle wave function with remarkable holonomy properties and a ground-state wave function with off-diagonal long-range order.

Coulomb gas approach to quantum Hall effect

We show that single and multiparticle wave functions for both electrons and anyons relevant to the QHE can be obtained in a consistent way using Coulomb gas conformal Vertex operators. The values of the allowed charges are determined by the periodicity properties of the collective correlation functions on the torus.

Quantum effects of electric fluxes in multiparticle systems

The electric Aharonov-Bohm single-particle phase shift is derived in the quasi-classical approximation by an analysis of the multiparticle closed system constituted by an incident particle and the source particles for the electric space-time flux. An explicit multiparticle wave function is given representing an electric Aharonov-Bohm system.