Many-particle Quantum Research Articles

Interaction picture density matrix quantum Monte Carlo.

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

Charge modulation as fingerprints of phase-string triggered interference

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high $T_c$ cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock type mean field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite $t-J$ ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

Exchange Coulomb interaction in nanotubes: Dispersion of Langmuir waves

The microscopic derivation of the Coulomb exchange interaction for electrons located on the nanotubes is presented. The derivation is based on the many-particle quantum hydrodynamic method. We demonstrate the effect of curvature of the nanocylinders on the force of exchange interaction. We calculate corresponding dispersion dependencies for electron oscillations on the nanotubes.

Equilibration and approximate conservation laws: Dipole oscillations and perfect drag of ultracold atoms in a harmonic trap

The presence of (approximate) conservation laws can prohibit the fast relaxation of interacting many-particle quantum systems. We investigate this physics by studying the center-of-mass oscillations of two species of fermionic ultracold atoms in a harmonic trap. If their trap frequencies are equal, a dynamical symmetry (spectrum generating algebra), closely related to Kohn's theorem, prohibits the relaxation of center-of-mass oscillations. A small detuning $\delta\omega$ of the trap frequencies for the two species breaks the dynamical symmetry and ultimately leads to a damping of dipole oscillations driven by inter-species interactions. Using memory-matrix methods, we calculate the relaxation as a function of frequency difference, particle number, temperature, and strength of inter-species interactions. When interactions dominate, there is almost perfect drag between the two species and the dynamical symmetry is approximately restored. The drag can either arise from Hartree potentials or from friction. In the latter case (hydrodynamic limit), the center-of-mass oscillations decay with a tiny rate, $1/\tau \propto (\delta\omega)^2/\Gamma$, where $\Gamma$ is a single particle scattering rate.

Nonparadoxical loss of information in black hole evaporation in a quantum collapse model

We consider a novel approach to address the black hole information paradox. The idea is based on adapting, to the situation at hand, the modified versions of quantum theory involving spontaneous stochastic dynamical collapse of quantum states, which have been considered in attempts to deal with shortcomings of the standard Copenhagen interpretation of quantum mechanics, in particular, the issue known as ``the measurement problem.'' The new basic hypothesis is that the modified quantum behavior is enhanced in the region of high curvature so that the information encoded in the initial quantum state of the matter fields is rapidly erased as the black hole singularity is approached. We show that in this manner the complete evaporation of the black hole via Hawking radiation can be understood as involving no paradox. Calculations are performed using a modified version of quantum theory known as ``continuous spontaneous localization'' (CSL), which was originally developed in the context of many-particle nonrelativistic quantum mechanics. We use a version of CSL tailored to quantum field theory and applied in the context of the two -dimensional Callan-Giddings-Harvey-Strominger model. Although the role of quantum gravity in this picture is restricted to the resolution of the singularity, related studies suggest that there might be further connections.

Stochastic limit method and interference in quantum many-particle systems

We consider the problem of excitation energy transfer in quantum many-particle systems with a dipole interaction. The considered exciton transfer mechanism is based on quantum interference. We show that by a special choice of interaction parameters, an enhancement of the exciton transfer to a sink and suppression of the transfer to alternative sinks can be achieved. The enhancement is proportional to the number of particles in the system. We use the quantum stochastic limit method to describe the dynamics. We indicate possible applications of the proposed mechanism to quantum processes in photosynthesis.

Stochastic limit method and interference in quantum many-particle systems

Для многочастичных квантовых систем с дипольным взаимодействием с квантовым полем рассмотрена проблема транспорта энергии электронного возбуждения при помощи механизма экситонного переноса, основанного на квантовой интерференции. Показано, что при специальном выборе параметров взаимодействия в модели квантового графа можно достичь усиления переноса экситона на сток, пропорционального числу частиц в системе, а также подавить перенос на альтернативные стоки. Для описания динамики используется метод квантового стохастического предела. Отмечены возможные применения указанного механизма в процессах квантового фотосинтеза.

Random matrix theory for transition strength densities in finite quantum systems: Results from embedded unitary ensembles

Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless fermion (or boson) systems, with say m fermions (or bosons) in N single particle states and interacting via k-body interactions, we have EGUE(k) [embedded GUE of k-body interactions] with GUE embedding and the embedding algebra is U(N). A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (then the initial and final systems are same), nuclear beta and double beta decay (then the initial and final systems are different), particle addition to or removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities (transition strengths multiplied by the density of states at the initial and final energies), we have derived formulas for the lower order bivariate moments of the strength densities generated by a variety of transition operators. Firstly, for a spinless fermion system, using EGUE(k) representation for a Hamiltonian that is k-body and an independent EGUE(t) representation for a transition operator that is t-body and employing the embedding U(N) algebra, finite-N formulas for moments up to order four are derived, for the first time, for the transition strength densities. Secondly, formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. In addition, moments formulas are also derived for a transition operator that removes k0 number of particles from a system of m spinless fermions. In the dilute limit, these formulas are shown to reduce to those for the EGOE version derived using the asymptotic limit theory of Mon and French (1975). Numerical results obtained using the exact formulas for two-body (k=2) Hamiltonians (in some examples for k=3 and 4) and the asymptotic formulas clearly establish that in general the smoothed (with respect to energy) form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.

Quantum kinetics of spinning neutral particles: General theory and Spin wave dispersion

Plasma physics gives an example of physical system of particles with the long-range interaction. At the small velocities of particles we can consider the plasmas approximately as the systems of particles with the Coulomb interaction. The Coulomb interaction is an isotropic interaction. Systems of spinning neutral particles are involved in the spin–spin interaction, which is a long-range anisotropic interparticle interaction. Therefore they can reveal more rich properties than the Coulomb plasmas. Furthermore, to study the systems of spinning particles we can develop the kinetic and hydrodynamic methods similar to the methods applying in the plasma physics. We derive the kinetic equations by a new method, which is the generalization of the many-particle quantum hydrodynamics. Obtained set of the kinetic equations is truncated, so we have a closed set of two equations. First of them is the kinetic equation for the quantum distribution function. The second equation is the equation for the spin-distribution function, which describes the spin kinetic evolution and contributes to the time evolution of the distribution function. Our method allows one to obtain equations for both the three dimensional systems of particles and the low dimensional systems. Hence we consider the spin waves in the three- and the two-dimensional systems of neutral spinning particles.

Improved Lieb-Oxford exchange-correlation inequality with a gradient correction

We prove a Lieb-Oxford-type inequality on the indirect part of the Coulomb energy of a general many-particle quantum state, with a lower constant than the original statement but involving an additional gradient correction. The result is similar to a recent inequality of Benguria, Bley and Loss, except that the correction term is purely local, which is more usual in density functional theory. In an appendix, we discuss the connection between the indirect energy and the classical Jellium energy for constant densities. We show that they differ by an explicit shift due to the long range of the Coulomb potential.

Exchange interaction effects on waves in magnetized quantum plasmas

We have applied the many-particle quantum hydrodynamics that includes the Coulomb exchange interaction to magnetized quantum plasmas. We considered a number of wave phenomena that are affected by the Coulomb exchange interaction. Since the Coulomb exchange interaction affects the longitudinal and transverse-longitudinal waves, we focused our attention on the Langmuir waves, the Trivelpiece-Gould waves, the ion-acoustic waves in non-isothermal magnetized plasmas, the dispersion of the longitudinal low-frequency ion-acoustic waves, and low-frequency electromagnetic waves at Te ≫ Ti. We have studied the dispersion of these waves and present the numeric simulation of their dispersion properties.

Applications of the Capelli identities in physics and representation theory

Capelli identities are shown to facilitate the construction of representations of various Heisenberg algebras that arise in many-particle quantum mechanics and the construction of holomorphic representations of many Lie algebras by vector coherent state methods. We consider the original Capelli identity and its generalizations by Turnbull and by Howe and Umeda.

One-Dimensional Filamentary Multiparticle Quantum Structures Arising in the Plane Transverse to External Homogeneous Magnetic Field

It is shown that a single-particle wave function Ψ, obtained (Landau, 1930) as a solution of the Schr?dinger equation (for a charged particle in a homogeneous magnetic field), and an operator relation of (or equation ) lead to the dynamic description of one-dimensional many-particle quantum filamentary states. Thus, one can overcome the problem, connected with the finding of many-body wave function as solution of the Schr?dinger equation with a very tangled Hamiltonian for multi-body system. An effect of nonlocality appears. The dependence of the linear density of particles on the magnetic field and on the number of particles in the one- dimension filamentary multiparticle quantum structure is calculated.

On the weak coupling limit of quantum many-body dynamics and the quantum Boltzmann equation

The rigorous derivation of the Uehling-Uhlenbeck equation from more fundamental quantum many-particle systems is a challenging open problem in mathematics. In this paper, we exam the weak coupling limit of quantum N-particle dynamics. We assume the integral of the microscopic interaction is zero and we assume W^{4,1} per-particle regularity on the coressponding BBGKY sequence so that we can rigorously commute limits and integrals. We prove that, if the BBGKY sequence does converge in some weak sense, then this weak-coupling limit must satisfy the infinite quantum Maxwell-Boltzmann hierarchy instead of the expected infinite Uehling-Uhlenbeck hierarchy, regardless of the statistics the particles obey. Our result indicates that, in order to derive the Uehling-Uhlenbeck equation, one must work with per-particle regularity bound below W^{4,1}.

Theory of self-resonance after inflation. II. Quantum mechanics and particle-antiparticle asymmetry

We further develop a theory of self-resonance after inflation in a large class of models involving multiple scalar fields. We concentrate on inflaton potentials that carry an internal symmetry, but also analyze weak breaking of this symmetry. This is the second part of a two-part series of papers. Here in part 2 we develop an understanding of the resonance structure from the underlying many-particle quantum mechanics. We begin with a small-amplitude analysis, which obtains the central resonant wave numbers, and relate it to perturbative processes. We show that the dominant resonance structure is determined by (i) the nonrelativistic scattering of many quantum particles and (ii) the application of Bose-Einstein statistics to the adiabatic and isocurvature modes, as introduced in part 1 [M. P. Hertzberg et al., Phys. Rev. D 90, 123528 (2014)]. Other resonance structures are understood in terms of annihilations and decays. We set up Bunch-Davies vacuum initial conditions during inflation and track the evolution of modes including Hubble expansion. In the case of a complex inflaton carrying an internal U(1) symmetry, we show that when the isocurvature instability is active, the inflaton fragments into separate regions of $\ensuremath{\phi}$-particles and anti-$\ensuremath{\phi}$-particles. We then introduce a weak breaking of the U(1) symmetry; this can lead to baryogenesis, as shown by some of us recently [M. P. Hertzberg and J. Karouby, Phys. Lett. B 737, 34 (2014); Phys. Rev. D 89, 063523 (2014)]. Then using our results, we compute corrections to the particle-antiparticle asymmetry from this preheating era.

“Light-Cone” Dynamics After Quantum Quenches in Spin Chains

Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.

Quantum metrology with Dicke squeezed states

We introduce a new class of quantum many-particle entangled states, called the Dicke squeezed (or DS) states, which can be used to improve the precision in quantum metrology beyond the standard quantum limit. We show that the enhancement in measurement precision is characterized by a single experimentally detectable parameter, called the Dicke squeezing , which also bounds the entanglement depth for this class of states. The measurement precision approaches the ultimate Heisenberg limit as attains the minimum in an ideal Dicke state. Compared with other entangled states, we show that the DS states are more robust to decoherence and give better measurement precision under typical experimental noise.

Focus on out-of-equilibrium dynamics in strongly interacting one-dimensional systems

In the past few years, there have been significant advances in understanding out-of-equilibrium dynamics in strongly interacting many-particle quantum systems. This is the case for 1D dynamics, where experimental advances—both with ultracold atomic gases and with solid state systems—have been accompanied by advances in theoretical methods, both analytical and numerical. This ‘focus on’ collection brings together 17 new papers, which together give a representative overview of the recent advances.

Low-energy spectrum of iron-sulfur clusters directly from many-particle quantum mechanics.

Iron-sulfur clusters are a universal biological motif. They carry out electron transfer, redox chemistry and even oxygen sensing, in diverse processes including nitrogen fixation, respiration and photosynthesis. Their low-lying electronic states are key to their remarkable reactivity, but they cannot be directly observed. Here, we present the first ever quantum calculation of the electronic levels of [2Fe-2S] and [4Fe-4S] clusters free from any model assumptions. Our results highlight the limitations of long-standing models of their electronic structure. In particular, we demonstrate that the widely used Heisenberg double exchange model underestimates the number of states by one to two orders of magnitude, which can conclusively be traced to the absence of Fe dd excitations, thought to be important in these clusters. Furthermore, the electronic energy levels of even the same spin are dense on the scale of vibrational fluctuations and this provides a natural explanation for the ubiquity of these clusters in catalysis in nature.

Nonlinear atom-photon-interaction-induced population inversion and inverted quantum phase transition of Bose-Einstein condensate in an optical cavity

In this paper we explore the rich structure of macroscopic many-particle quantum states for Bose- Einstein condensate in an optical cavity with the tunable nonlinear atom-photon interaction [Nature (London) 464, 1301 (2010)]. Population inversion, bistable normal phases and the coexistence of normal{superradiant phases are revealed by adjusting of the experimentally realizable interaction strength and pump-laser frequency. For the negative (effective) cavity-frequency we observe remark- ably an inverted quantum phase transition (QPT) from the superradiant to normal phases with the increase of atom-field coupling, which is just opposite to the QPT in the normal Dicke model. The bistable macroscopic states are derived analytically in terms of the spin-coherent-state variational method by taking into account of both normal and inverted pseudospin states.