Quantum many-body systems out of equilibrium
J. Eisert; M. Friesdorf; C. Gogolin
2015-09-01
Closed quantum many-body systems out of equilibrium pose several long-standing problems in physics. Recent years have seen a tremendous progress in approaching these questions, not least due to experiments with cold atoms and trapped ions in instances of quantum simulations. This article provides an overview on the progress in understanding dynamical equilibration and thermalisation of closed quantum many-body systems out of equilibrium due to quenches, ramps and periodic driving. It also addresses topics such as the eigenstate thermalisation hypothesis, typicality, transport, many-body localisation, universality near phase transitions, and prospects for quantum simulations.
Distinguishing Quantum and Classical Many-Body Systems
Dvir Kafri; Jacob Taylor
2015-04-06
Controllable systems relying on quantum behavior to simulate distinctly quantum models so far rely on increasingly challenging classical computing to verify their results. We develop a general protocol for confirming that an arbitrary many-body system, such as a quantum simulator, can entangle distant objects. The protocol verifies that distant qubits interacting separately with the system can become mutually entangled, and therefore serves as a local test that excitations of the system can create non-local quantum correlations. We derive an inequality analogous to Bell's inequality which can only be violated through entanglement between distant sites of the many-body system. Although our protocol is applicable to general many-body systems, it requires finding system-dependent local operations to violate the inequality. A specific example in quantum magnetism is presented.
Measure synchronization in quantum many-body systems
Haibo Qiu; Bruno Julia-Diaz; Miguel Angel Garcia-March; Artur Polls
2014-10-24
The concept of measure synchronization between two coupled quantum many-body systems is presented. In general terms we consider two quantum many-body systems whose dynamics gets coupled through the contact particle-particle interaction. This coupling is shown to produce measure synchronization, a generalization of synchrony to a large class of systems which takes place in absence of dissipation. We find that in quantum measure synchronization, the many-body quantum properties for the two subsystems, e.g. condensed fractions and particle fluctuations, behave in a coordinated way. To illustrate the concept we consider a simple case of two species of bosons occupying two distinct quantum states. Measure synchronization can be readily explored with state-of-the-art techniques in ultracold atomic gases and, if propertly controlled, be employed to share quantum correlations between different degrees of freedom.
Entanglement dynamics in quantum many-body systems
Wen Wei Ho; Dmitry A. Abanin
2015-08-16
We study entanglement growth in quantum many-body systems and propose a method to experimentally measure it. We show that entanglement growth is related to the spreading of local operators. In ergodic systems, linear spreading of operators results in a universal, linear in time growth of entanglement for initial product states, in contrast to the logarithmic growth of entanglement in many-body localized (MBL) systems. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of many copies of the original system, subject to a perturbation that reconnects different parts of the system. Exponential decay of the Loschmidt echo, characteristic of ergodic systems, implies linear growth of entanglement. Our proposal to experimentally measure entanglement growth uses a quantum switch (two-level system) which controls connections in the composite system. By measuring only the switch's dynamics, the growth of the R\\'enyi entropies can be extracted. Our work provides a way to directly probe dynamical properties of many-body systems, in particular, allowing for a direct observation of many-body localization.
Universal Behavior beyond Multifractality in Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Luitz, David J.; Alet, Fabien; Laflorencie, Nicolas
2014-02-01
How many states of a configuration space contribute to a wave function? Attempts to answer this ubiquitous question have a long history in physics and are keys to understanding, e.g., localization phenomena. Beyond single-particle physics, a quantitative study of the ground state complexity for interacting many-body quantum systems is notoriously difficult, mainly due to the exponential growth of the configuration (Hilbert) space with the number of particles. Here we develop quantum Monte Carlo schemes to overcome this issue, focusing on Shannon-Rényi entropies of ground states of large quantum many-body systems. Our simulations reveal a generic multifractal behavior while the very nature of quantum phases of matter and associated transitions is captured by universal subleading terms in these entropies.
Entanglement dynamics in quantum many-body systems
Ho, Wen Wei
2015-01-01
We study entanglement growth in quantum many-body systems and propose a method to experimentally measure it. We show that entanglement growth is related to the spreading of local operators. In ergodic systems, linear spreading of operators results in a universal, linear in time growth of entanglement for initial product states, in contrast to the logarithmic growth of entanglement in many-body localized (MBL) systems. Furthermore, we show that entanglement growth is directly related to the decay of the Loschmidt echo in a composite system comprised of many copies of the original system, subject to a perturbation that reconnects different parts of the system. Exponential decay of the Loschmidt echo, characteristic of ergodic systems, implies linear growth of entanglement. Our proposal to experimentally measure entanglement growth uses a quantum switch (two-level system) which controls connections in the composite system. By measuring only the switch's dynamics, the growth of the R\\'enyi entropies can be extrac...
On microstates counting in many body polymer quantum systems
Chacon-Acosta, Guillermo; Morales-Tecotl, Hugo A. [Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Mexico D. F. 09340 (Mexico); Dagdug, Leonardo [Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892 (United States); Departamento de Fisica, Universidad Autonoma Metropolitana-Iztapalapa, Mexico D. F. 09340 (Mexico)
2011-10-14
Polymer quantum systems are mechanical models quantized in a similar way as loop quantum gravity but in which loops/graphs resembling polymers are replaced by discrete sets of points. Such systems have allowed to study in a simpler context some novel aspects of loop quantum gravity. Although thermal aspects play a crucial role in cosmology and black hole physics little attention has been given to the thermostatistics of many body polymer quantum systems. In this work we explore how the features of a one-dimensional effective polymer gas, affect its microstate counting and hence the corresponding thermodynamical quantities.
Experimental Quantum Simulation of Entanglement in Many-body Systems
Jingfu Zhang; Tzu-Chieh Wei; Raymond Laflamme
2011-07-25
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a small-size system already displays singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
Relativistic Quantum Dynamics of Many-Body Systems
F. Coester; W. N. Polyzou
2001-02-22
Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract framework of four dimensional Euclidean Green functions that can be used to construct relativistic quantum dynamics of N-particle systems consistent with these requirements. This approach should be useful in bridging the gap between few-body dynamics based on phenomenological mass operators and on quantum field theory.
Thermalization and ergodicity in many-body open quantum systems
Znidaric, Marko; Benenti, Giuliano; Casati, Giulio; Rossini, Davide
2009-01-01
We study thermalization in many-body quantum systems locally coupled to an external bath. It is shown that quantum chaotic systems do thermalize, that is, they exhibit relaxation to an invariant ergodic state which, in the bulk, is well approximated by the grand canonical state. Moreover, the resulting ergodic state in the bulk does not depend on the details of the baths. On the other hand, for integrable systems the invariant state does depend on the bath and is different from the grand canonical state.
Boundary driven open quantum many-body systems
Prosen, Tomaž
2014-01-08
In this lecture course I outline a simple paradigm of non-eqjuilibrium quantum statistical physics, namely we shall study quantum lattice systems with local, Hamiltonian (conservative) interactions which are coupled to the environment via incoherent processes only at the system's boundaries. This is arguably the simplest nontrivial context where one can study far from equilibrium steady states and their transport properties. We shall formulate the problem in terms of a many-body Markovian master equation (the so-called Lindblad equation, and some of its extensions, e.g. the Redfield eqaution). The lecture course consists of two main parts: Firstly, and most extensively we shall present canonical Liouville-space many-body formalism, the so-called 'third quantization' and show how it can be implemented to solve bi-linear open many-particle problems, the key peradigmatic examples being the XY spin 1/2 chains or quasi-free bosonic (or harmonic) chains. Secondly, we shall outline several recent approaches on how to approach exactly solvable open quantum interacting many-body problems, such as anisotropic Heisenberg ((XXZ) spin chain or fermionic Hubbard chain.
Frustration, Entanglement, and Correlations in Quantum Many Body Systems
U. Marzolino; S. M. Giampaolo; F. Illuminati
2013-04-30
We derive an exact lower bound to a universal measure of frustration in degenerate ground states of quantum many-body systems. The bound results in the sum of two contributions: entanglement and classical correlations arising from local measurements. We show that average frustration properties are completely determined by the behavior of the maximally mixed ground state. We identify sufficient conditions for a quantum spin system to saturate the bound, and for models with twofold degeneracy we prove that average and local frustration coincide.
Quantum Control of Many-Body Systems by the Density
S. E. B. Nielsen; M. Ruggenthaler; R. van Leeuwen
2014-12-11
In this work we focus on a recently introduced method [1] to construct the external potential $v$ that, for a given initial state, produces a prescribed time-dependent density in an interacting quantum many-body system. We show how this method can also be used to perform flexible and efficient quantum control. The simple interpretation of the density (the amount of electrons per volume) allows us to use our physical intuition to consider interesting control problems and to easily restrict the search space in optimization problems. The method's origin in time-dependent density-functional theory makes studies of large systems possible. We further discuss the generalization of the method to higher dimensions and its numerical implementation in great detail. We also present several examples to illustrate the flexibility, and to confirm that the scheme is efficient and stable even for large and rapid density variations irrespective of the initial state and interactions.
Many-Body Localization in Imperfectly Isolated Quantum Systems
NASA Astrophysics Data System (ADS)
Johri, Sonika; Nandkishore, Rahul; Bhatt, R. N.
2015-03-01
We use numerical exact diagonalization to analyze which aspects of the many-body localization phenomenon survive in an imperfectly isolated setting, when the system of interest is weakly coupled to a thermalizing environment. We show that widely used diagnostics (such as many-body level statistics and expectation values in exact eigenstates) cease to show signatures of many-body localization above a critical coupling that is exponentially small in the size of the environment. However, we also identify alternative diagnostics for many-body localization, in the spectral functions of local operators. Diagnostics include a discrete spectrum and a hierarchy of energy gaps, including a universal gap at zero frequency. These alternative diagnostics are shown to be robust, and continue to show signatures of many-body localization as long as the coupling to the bath is weaker than the characteristic energy scales in the system. We also examine how these signatures disappear when the coupling to the environment becomes larger than the characteristic energy scales of the system.
Geometric methods for nonlinear many-body quantum systems
Mathieu Lewin
2010-12-10
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\\'nski and G\\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and prove nonlinear versions of the HVZ theorem, in the spirit of works of Friesecke. In the last section we study translation-invariant many-body systems comprising a nonlinear term, which effectively describes the interactions with a second system. As an example, we prove the existence of the multi-polaron in the Pekar-Tomasevich approximation, for certain values of the coupling constant.
Quantum phase transition in strongly correlated many-body system
NASA Astrophysics Data System (ADS)
You, Wenlong
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions (QPTs), driven by experimental advance on the cuprate superconductors, the heavy fermion materials, organic conductors, Quantum Hall effect, Fe-As based superconductors and other related compounds. It is clear that strong electronic interactions play a crucial role in the systems of current interest, and simple paradigms for the behavior of such systems near quantum critical points remain unclear. Furthermore, the rapid progress in Feshbach resonance and optical lattice provides a flexible platform to study QPT. Quantum Phase Transition (QPT) describes the non-analytic behaviors of the ground-state properties in a many-body system by varying a physical parameter at absolute zero temperature - such as magnetic field or pressure, driven by quantum fluctuations. Such quantum phase transitions can be first-order phase transition or continuous. The phase transition is usually accompanied by a qualitative change in the nature of the correlations in the ground state, and describing this change shall clearly be one of our major interests. We address this issue from three prospects in a few strong correlated many-body systems in this thesis, i.e., identifying the ordered phases, studying the properties of different phases, characterizing the QPT points. In chapter 1, we give an introduction to QPT, and take one-dimensional XXZ model as an example to illustrate the QPT therein. Through this simple example, we would show that when the tunable parameter is varied, the system evolves into different phases, across two quantum QPT points. The distinct phases exhibit very different behaviors. Also a schematic phase diagram is appended. In chapter 2, we are engaged in research on ordered phases. Originating in the work of Landau and Ginzburg on second-order phase transition, the spontaneous symmetry breaking induces nonzero expectation of field operator, e.g., magnetization M in the Ising model, and then we say long range order (LRO) exists in the system. LRO plays a key role in determining the ordered-disorder transition. Thereby, we investigate two-dimensional 120° orbital-only model to present how to extract the information of LRO in a pedagogical manner, by applying the reflection positivity method introduced by Dyson, Lieb, and Simon. We rigorously establish the existence of an anti-ferromagnetic like transverse orbital long-range order in the so called two-dimensional 120° model at zero temperature. Next we consider possible pairings in the family of FeAs-based ReO1--xFxFeAs (Re=La, Nd, Ce, Pr, etc.) high-temperature superconductors. We build some identities based on a two-orbital model, and obtained some constraints on a few possible pairings. We also establish the sufficient conditions for the coexistence of two superconducting orders, and we propose the most favorable pairings around half filling according to physical consideration. In chapter 3, we present a quantum solvation process with solvent of fermion character based on the one-dimensional asymmetric t-J-Jz model. The model is experimental realizable in optical lattices and exhibits rich physics. In this work, we show that there exist two types of phase separations, one is driven by potential energy while the other by kinetic energy. In between, solvation process occurs. Analytically, we are able to obtain some rigorous results to understand the underlying physics. Numerically, we perform exact diagonalization and density matrix renormalization group calculations, accompanied by detailed finite size analysis. In chapter 4, we explore several characterizations of QPT points. As distinguished from the methods in condensed-matter physics, we give much attention to understand QPT from the quantum information (QI) point of view. The perspective makes a new bridge between these two fields. It no only can facilitate the understanding of condensed-matter physics, but also provide the prominent playground for the quantum information theory. They are fidelity susceptibility a
The approach to typicality in many-body quantum systems
Shawn Dubey; Luciano Silvestri; Justin Finn; Sai Vinjanampathy; Kurt Jacobs
2011-12-15
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization. Here we give numerical evidence that many-body lattice systems generically approach typicality as the number of subsystems is increased, and thus provide further support for the eigenstate thermalization hypothesis. Our results indicate that the deviation of many-body systems from typicality decreases exponentially with the number of systems. Further, by averaging over a number of randomly-selected nearest-neighbor interactions, we obtain a power-law for the atypicality as a function of the Hilbert space dimension, distinct from the power-law possessed by random Hamiltonians.
Approach to typicality in many-body quantum systems.
Dubey, Shawn; Silvestri, Luciano; Finn, Justin; Vinjanampathy, Sai; Jacobs, Kurt
2012-01-01
The recent discovery that for large Hilbert spaces, almost all (that is, typical) Hamiltonians have eigenstates that place small subsystems in thermal equilibrium, has shed much light on the origins of irreversibility and thermalization. Here we give numerical evidence that many-body lattice systems generically approach typicality as the number of subsystems is increased, and thus provide further support for the eigenstate thermalization hypothesis. Our results indicate that the deviation of many-body systems from typicality decreases exponentially with the number of systems. Further, by averaging over a number of randomly selected nearest-neighbor interactions, we obtain a powerlaw for the atypicality as a function of the Hilbert space dimension, distinct from the power law possessed by random Hamiltonians. PMID:22400546
Single shot simulations of dynamic quantum many-body systems
Kaspar Sakmann; Mark Kasevich
2015-01-14
The single-particle density is the most basic quantity that can be calculated from a given many-body wave function. It provides the probability to find a particle at a given position when the average over many realizations of an experiment is taken. However, the outcome of single experimental shots of ultracold atom experiments is determined by the $N$-particle probability density. This difference can lead to surprising results. For example, independent Bose-Einstein condensates (BECs) with definite particle numbers form interference fringes even though no fringes would be expected based on the single-particle density [1-4]. By drawing random deviates from the $N$-particle probability density single experimental shots can be simulated from first principles [1, 3, 5]. However, obtaining expressions for the $N$-particle probability density of realistic time-dependent many-body systems has so far been elusive. Here, we show how single experimental shots of general ultracold bosonic systems can be simulated based on numerical solutions of the many-body Schr\\"odinger equation. We show how full counting distributions of observables involving any number of particles can be obtained and how correlation functions of any order can be evaluated. As examples we show the appearance of interference fringes in interacting independent BECs, fluctuations in the collisions of strongly attractive BECs, the appearance of randomly fluctuating vortices in rotating systems and the center of mass fluctuations of attractive BECs in a harmonic trap. The method described is broadly applicable to bosonic many-body systems whose phenomenology is driven by information beyond what is typically available in low-order correlation functions.
Dissipation and dynamics in quantum many-body systems
NASA Astrophysics Data System (ADS)
Barker, Brent Wendolyn
In this thesis, we simulate the time evolution of quantum many-body systems and use comparisons to experimental data in order to learn more about the properties of nuclear matter and understand better the dynamical processes in central nuclear collisions. We further advance the development of a nonequilibrium Green's function description of both central nuclear collisions and Bose-Einstein Condensates. First in the thesis, we determine the viscosity of nuclear matter by adjusting the in-medium nucleon-nucleon cross section (IMNNCS) in our BUU transport model until the simulation results match experimental data on nuclear stopping in central nuclear collisions at intermediate energies. Then we use that cross section to calculate the viscosity self-consistently. We also calculate the ratio of shear viscosity to entropy density to determine how close the system is to the proposed universal quantum lower limit. Next, we use the same BUU transport model to isolate the protons emitted early in a central nuclear collision at intermediate energy, as predicted in the model, using a filter on high transverse momentum, and we show the effect on the source function. We predict a recontraction of protons at late times in the central collision of 112Sn+112Sn at 50 MeV/nucleon that results in a resurgence of emission of protons and show how to use the transverse momentum filter and the source function to test this prediction in experiment. Next, we develop an early implementation of a more fully quantal transport model than the BUU equations, with our sights set on solving central nuclear collisions in 3D using nonequilibrium Green's functions. In our 1D, mean field, density matrix model, we demonstrate the initial state preparation and collision of 1D nuclear "slabs". With the aim of reducing the computational cost of the calculation, we show that we can neglect far off-diagonal elements in the density matrix without affecting the one-body observables. Further, we describe a method of recasting the density matrix in a rotated coordinate system, enabling us to not only ignore the irrelevant matrix elements in the time evolution, but also avoid computing them completely, reducing the computational cost. As an added benefit, we find that the rotation allows us to partially decouple the position and momentum discretization, permitting access to arbitrary regimes of kinetic energy without altering the resolution and range of the 1D box in position space. Finally, we exhibited the wide applicability of this density matrix approach by applying it to a system of 2000 ultracold 87Rb atoms in a Bose-Einstein condensate, as described by the Gross-Pitaevskii equation, successfully achieving a stable state in a harmonic oscillator trap.
General coordinate invariance in quantum many-body systems
Tomas Brauner; Solomon Endlich; Alexander Monin; Riccardo Penco
2014-10-21
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the background metric and gauge fields, first introduced by Son and Wingate in 2005 and refined in subsequent works, follow naturally from our framework. Our approach makes it clear that Galilei or Poincare symmetry is by no means a necessary prerequisite for making the theory invariant under coordinate diffeomorphisms. General covariance merely expresses the freedom to choose spacetime coordinates at will, whereas the true, physical symmetries of the system can be separately implemented as "internal" symmetries within the vielbein formalism. A systematic way to implement such symmetries is provided by the coset construction. We illustrate this point by applying our formalism to nonrelativistic s-wave superfluids.
Characterizing and Quantifying Frustration in Quantum Many-Body Systems
S. M. Giampaolo; G. Gualdi; A. Monras; F. Illuminati
2012-01-05
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.
Quantum variance: a measure of quantum coherence and quantum correlations for many-body systems
Irénée Frérot; Tommaso Roscilde
2015-09-22
Quantum coherence is a fundamental common trait of quantum phenomena, from the interference of matter waves to quantum degeneracy of identical particles. Despite its importance, estimating and measuring quantum coherence in generic, mixed many-body quantum states remains a formidable challenge, with fundamental implications in areas as broad as quantum condensed matter, quantum information, quantum metrology, and quantum biology. Here we provide a quantitative definition of the variance of quantum coherent fluctuations (the \\emph{quantum variance}) of any observable on generic quantum states. The quantum variance generalizes the concept of thermal de Broglie wavelength (for the position of a free quantum particle) to the space of eigenvalues of any observable, quantifying the degree of coherent delocalization in that space. The quantum variance is generically measurable and computable as the difference between the static fluctuations and the static susceptibility of the observable, despite its simplicity, it is found to provide a tight lower bound to most widely accepted estimators of "quantumness" of observables (both as a feature as well as a resource), such as the Wigner-Yanase skew information and the quantum Fisher information. When considering bipartite fluctuations in an extended quantum system, the quantum variance expresses genuine quantum correlations (of discord type) among the two parts. In the case of many-body systems it is found to obey an area law at finite temperature, extending therefore area laws of entanglement and quantum fluctuations of pure states to the mixed-state context. Hence the quantum variance paves the way to the measurement of macroscopic quantum coherence and quantum correlations in most complex quantum systems.
Absorbing boundary conditions for dynamical many-body quantum systems
Sølve Selstø; Simen Kvaal
2010-01-28
In numerical studies of the dynamics of unbound quantum mechanical systems, absorbing boundary conditions are frequently applied. Although this certainly provides a useful tool in facilitating the description of the system, its applications to systems consisting of more than one particle is problematic. This is due to the fact that all information about the system is lost upon absorption of one particle; a formalism based solely on the Scrh{\\"o}dinger equation is not able to describe the remainder of the system as particles are lost. Here we demonstrate how the dynamics of a quantum system with a given number of identical fermions may be described in a manner which allows for particle loss. A consistent formalism which incorporates the evolution of sub-systems with a reduced number of particles is constructed through the Lindblad equation. Specifically, the transition from an $N$-particle system to an $(N-1)$-particle system due to a complex absorbing potential is achieved by relating the Lindblad operators to annihilation operators. The method allows for a straight forward interpretation of how many constituent particles have left the system after interaction. We illustrate the formalism using one-dimensional two-particle model problems.
Localization and Glassy Dynamics Of Many-Body Quantum Systems
Carleo, Giuseppe; Becca, Federico; Schiró, Marco; Fabrizio, Michele
2012-01-01
When classical systems fail to explore their entire configurational space, intriguing macroscopic phenomena like aging and glass formation may emerge. Also closed quanto-mechanical systems may stop wandering freely around the whole Hilbert space, even if they are initially prepared into a macroscopically large combination of eigenstates. Here, we report numerical evidences that the dynamics of strongly interacting lattice bosons driven sufficiently far from equilibrium can be trapped into extremely long-lived inhomogeneous metastable states. The slowing down of incoherent density excitations above a threshold energy, much reminiscent of a dynamical arrest on the verge of a glass transition, is identified as the key feature of this phenomenon. We argue that the resulting long-lived inhomogeneities are responsible for the lack of thermalization observed in large systems. Such a rich phenomenology could be experimentally uncovered upon probing the out-of-equilibrium dynamics of conveniently prepared quantum states of trapped cold atoms which we hereby suggest. PMID:22355756
Dissipative effects in dipolar, quantum many-body systems
NASA Astrophysics Data System (ADS)
Safavi-Naini, Arghavan; Capogrosso-Sansone, Barbara; Rey, Ana Maria
2015-03-01
We use Quantum Monte Carlo simulations, by the Worm algorithm, to study the ground state phase diagram of two-dimensional, dipolar lattice bosons where each site is coupled, via density operators, to an external reservoir. A recent related study of the XXZ model with ohmic coupling to an external reservoir reported the existence of a bath-induced Bose metal phase in the ground state phase diagram away from half filling, and a Luttinger liquid and a charge density wave at half-filling. Our work extends this methodology to higher dimensional systems with long-range interactions. In the case of hard-core bosons, our method can be applied to experimental systems featuring dipolar fermionic molecules in the presence of losses. This work utilized the Janus supercomputer, which is supported by the NSF (award number CNS-0821794) and the University of Colorado Boulder, and is a joint effort with the University of Colorado Denver and the National Center for Atmospheric Research, as well as OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma. NIST, JILA-NSF-PFC-1125844, NSF-PIF-1211914, NSF-PHY11-25915, ARO, ARO-DARPA-OLE, AFOSR, AFOSR-MURI.
Quantum effects in many-body gravitating systems
Golovko, V A
2015-01-01
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadro's number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the at...
Quantum effects in many-body gravitating systems
V. A. Golovko
2015-04-07
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadro's number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the atmosphere decreases as its mass increases. If short-range intermolecular forces are taken into account, the results obtained hold for excited states whose lifetime can however be very long. The results of the paper can be utilized for explaining the first stage of formation of celestial bodies from interstellar and even intergalactic gases.
A quantum many-body spin system in an optical lattice clock.
Martin, M J; Bishof, M; Swallows, M D; Zhang, X; Benko, C; von-Stecher, J; Gorshkov, A V; Rey, A M; Ye, Jun
2013-08-01
Strongly interacting quantum many-body systems arise in many areas of physics, but their complexity generally precludes exact solutions to their dynamics. We explored a strongly interacting two-level system formed by the clock states in (87)Sr as a laboratory for the study of quantum many-body effects. Our collective spin measurements reveal signatures of the development of many-body correlations during the dynamical evolution. We derived a many-body Hamiltonian that describes the experimental observation of atomic spin coherence decay, density-dependent frequency shifts, severely distorted lineshapes, and correlated spin noise. These investigations open the door to further explorations of quantum many-body effects and entanglement through use of highly coherent and precisely controlled optical lattice clocks. PMID:23929976
COVER IMAGE How quantum many-body systems
Loss, Daniel
Graphene spintronics Non-magnetic spin measurement Letter p313 Quantum phononics A ripple of excitement and A. Kanigel 313 Nonlinear detection of spin currents in graphene with non-magnetic electrodes Ivan J J. Millis and Silke Biermann 338 Local probing of propagating acoustic waves in a gigahertz echo
Schrieffer-Wolff transformation for quantum many-body systems
Bravyi, Sergey, E-mail: sbravyi@us.ibm.com [IBM Watson Research Center, Yorktown Heights, NY 10598 (United States); DiVincenzo, David P., E-mail: d.divincenzo@fz-juelich.de [RWTH Aachen and Forschungszentrum Juelich (Germany); Loss, Daniel, E-mail: Daniel.Loss@unibas.ch [Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel (Switzerland)
2011-10-15
The Schrieffer-Wolff (SW) method is a version of degenerate perturbation theory in which the low-energy effective Hamiltonian H{sub eff} is obtained from the exact Hamiltonian by a unitary transformation decoupling the low-energy and high-energy subspaces. We give a self-contained summary of the SW method with a focus on rigorous results. We begin with an exact definition of the SW transformation in terms of the so-called direct rotation between linear subspaces. From this we obtain elementary proofs of several important properties of H{sub eff} such as the linked cluster theorem. We then study the perturbative version of the SW transformation obtained from a Taylor series representation of the direct rotation. Our perturbative approach provides a systematic diagram technique for computing high-order corrections to H{sub eff}. We then specialize the SW method to quantum spin lattices with short-range interactions. We establish unitary equivalence between effective low-energy Hamiltonians obtained using two different versions of the SW method studied in the literature. Finally, we derive an upper bound on the precision up to which the ground state energy of the nth-order effective Hamiltonian approximates the exact ground state energy. - Highlights: > The Schrieffer-Wolff transformation is specialized to quantum spin lattices with short-range interactions. > We provide a diagram technique for computing high-order corrections to the effective low-energy Hamiltonian. > We derive a rigorous bound on the error up to which the nth-order effective low-energy dynamics approximates the exact dynamics.
Gauge equivalence among quantum nonlinear many body systems
A. M. Scarfone
2011-03-04
Transformations performing on the dependent and/or the independent variables are an useful method used to classify PDE in class of equivalence. In this paper we consider a large class of U(1)-invariant nonlinear Schr\\"odinger equations containing complex nonlinearities. The U(1) symmetry implies the existence of a continuity equation for the particle density $\\rho\\equiv|\\psi|^2$ where the current ${\\bfm j}_{_\\psi}$ has, in general, a nonlinear structure. We introduce a nonlinear gauge transformation on the dependent variables $\\rho$ and ${\\bfm j}_{\\psi}$ which changes the evolution equation in another one containing only a real nonlinearity and transforms the particle current ${\\bfm j}_{_\\psi}$ in the standard bilinear form. We extend the method to U(1)-invariant coupled nonlinear Schr\\"odinger equations where the most general nonlinearity is taken into account through the sum of an Hermitian matrix and an anti-Hermitian matrix. By means of the nonlinear gauge transformation we change the nonlinear system in another one containing only a purely Hermitian nonlinearity. Finally, we consider nonlinear Schr\\"odinger equations minimally coupled with an Abelian gauge field whose dynamics is governed, in the most general fashion, through the Maxwell-Chern-Simons equation. It is shown that the nonlinear transformation we are introducing can be applied, in this case, separately to the gauge field or to the matter field with the same final result. In conclusion, some relevant examples are presented to show the applicability of the method.
Observation of entanglement propagation in a quantum many-body system
Jurcevic, P; Hauke, P; Hempel, C; Zoller, P; Blatt, R; Roos, C F
2014-01-01
The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is ...
Quantum Field Theory of Many-body Systems from the Origin of Sound
Wen, Xiao-Gang
Quantum Field Theory of Many-body Systems from the Origin of Sound to an Origin of Light. It is useful to organize our discussion using the analogy to the well understood theory of quantum par- ticles words, a string condensed state is a quantum liquid of large strings. We would like to have a theory
Quantum Phase Space, Quantization Hierarchy, and Eclectic Quantum Many-Body System
Dong-Sheng Wang
2014-10-05
An operator-valued quantum phase space formula is constructed. The phase space formula of Quantum Mechanics provides a natural link between first and second quantization, thus contributing to the understanding of quantization problem. By the combination of quantization and hamiltonization of dynamics, a quantization hierarchy is introduced, beyond the framework of first and second quantization and generalizing the standard quantum theory. We apply our quantization method to quantum many-body system and propose an eclectic model, in which the dimension of Hilbert space does not scale exponentially with the number of particles due to the locality of interaction, and the evolution is a constrained Hamiltonian dynamics.
A scalable method for measuring entanglement entropy of quantum many-body systems
NASA Astrophysics Data System (ADS)
Tai, Eric; Lukin, Alex; Preiss, Philipp; Rispoli, Matthew; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2015-05-01
Quantum many-body systems far from equilibrium are challenging to understand due to the spreading of quantum correlations among the constituents. Measuring the entanglement growth in such a system can serve to characterize the dynamical phases. We use high precision optical potentials in a quantum gas microscope to investigate quench dynamics and entanglement of a few-body bosonic system. The entanglement entropy is directly estimated by interfering two identically prepared copies of the same dynamical state, in a many-body extension of the two particle Hong-Ou-Mandel interference of bosons. This approach provides a versatile and scalable protocol for investigating the purity and entanglement growth of our system.
Quantum simulation. Coherent imaging spectroscopy of a quantum many-body spin system.
Senko, C; Smith, J; Richerme, P; Lee, A; Campbell, W C; Monroe, C
2014-07-25
Quantum simulators, in which well-controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics inaccessible to modeling with classical computers. However, checking the results of such simulations also becomes classically intractable as system sizes increase. Here, we introduce and implement a coherent imaging spectroscopic technique, akin to magnetic resonance imaging, to validate a quantum simulation. We use this method to determine the energy levels and interaction strengths of a fully connected quantum many-body system. Additionally, we directly measure the critical energy gap near a quantum phase transition. We expect this general technique to become a verification tool for quantum simulators once experiments advance beyond proof-of-principle demonstrations and exceed the resources of conventional computers. PMID:25061207
Physics in one dimension: theoretical concepts for quantum many-body systems.
Schönhammer, K
2013-01-01
Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept. PMID:23220952
Hamiltonian tomography for quantum many-body systems with arbitrary couplings
NASA Astrophysics Data System (ADS)
Wang, Sheng-Tao; Deng, Dong-Ling; Duan, L.-M.
2015-09-01
Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body Hamiltonian with arbitrary long-range interactions, provided the energy density of the Hamiltonian remains finite. Different from quantum process tomography, our scheme is fully scalable with the number of qubits as the required rounds of measurements increase only linearly with the number of coupling terms in the Hamiltonian. The scheme makes use of synchronized dynamical decoupling pulses to simplify the many-body dynamics so that the unknown parameters in the Hamiltonian can be retrieved one by one. We simulate the performance of the scheme under the influence of various pulse errors and show that it is robust to typical noise and experimental imperfections.
Partial and quasi dynamical symmetries in quantum many-body systems
NASA Astrophysics Data System (ADS)
Leviatan, A.
2015-04-01
We introduce the notions of partial dynamical symmetry (PDS) and quasi dynamical symmetry (QDS) and demonstrate their relevance to nuclear spectroscopy, to quantum phase transitions and to mixed systems with regularity and chaos. The analysis serves to highlight the potential role of PDS and QDS towards understanding the emergent “simplicity out of complexity” exhibited by complex many-body systems.
Efficient simulation of one-dimensional quantum many-body systems
G. Vidal
2003-10-14
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved in the simulated evolution. Numerical analysis indicate that this method can be used, for instance, to efficiently compute time-dependent properties of low-energy dynamics of sufficiently regular but otherwise arbitrary one-dimensional quantum many-body systems.
NON-EQUILIBRIUM DYNAMICS OF MANY-BODY QUANTUM SYSTEMS: FUNDAMENTALS AND NEW FRONTIER
DeMille, David; LeHur, Karyn
2013-11-27
Rapid progress in nanotechnology and naofabrication techniques has ushered in a new era of quantum transport experiments. This has in turn heightened the interest in theoretical understanding of nonequilibrium dynamics of strongly correlated quantum systems. This project has advanced the frontiers of understanding in this area along several fronts. For example, we showed that under certain conditions, quantum impurities out of equilibrium can be reformulated in terms of an effective equilibrium theory; this makes it possible to use the gamut of tools available for quantum systems in equilibrium. On a different front, we demonstrated that the elastic power of a transmitted microwave photon in circuit QED systems can exhibit a many-body Kondo resonance. We also showed that under many circumstances, bipartite fluctuations of particle number provide an effective tool for studying many-body physics—particularly the entanglement properties of a many-body system. This implies that it should be possible to measure many-body entanglement in relatively simple and tractable quantum systems. In addition, we studied charge relaxation in quantum RC circuits with a large number of conducting channels, and elucidated its relation to Kondo models in various regimes. We also extended our earlier work on the dynamics of driven and dissipative quantum spin-boson impurity systems, deriving a new formalism that makes it possible to compute the full spin density matrix and spin-spin correlation functions beyond the weak coupling limit. Finally, we provided a comprehensive analysis of the nonequilibrium transport near a quantum phase transition in the case of a spinless dissipative resonant-level model. This project supported the research of two Ph.D. students and two postdoctoral researchers, whose training will allow them to further advance the field in coming years.
Ultracold atoms in optical lattices: tunable quantum many-body systems
W. Hofstetter
2006-01-01
Cold atoms in optical lattices offer an exciting new laboratory where quantum many-body phenomena can be realized in a highly controlled way. They can even serve as quantum simulators for notoriously difficult problems like high-temperature superconductivity. This review is focussed on the recent developments and new results in multi-component systems. Fermionic atoms with SU(N) symmetry have exotic superfluid and flavor-ordered
Editorial: Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems
NASA Astrophysics Data System (ADS)
Cazalilla, M. A.; Rigol, M.
2010-05-01
The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and understand many-body quantum systems. This focus issue of New Journal Physics brings together both experimentalists and theoreticians working on these problems to provide a comprehensive picture of the state of the field. Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems Contents Spin squeezing of high-spin, spatially extended quantum fields Jay D Sau, Sabrina R Leslie, Marvin L Cohen and Dan M Stamper-Kurn Thermodynamic entropy of a many-body energy eigenstate J M Deutsch Ground states and dynamics of population-imbalanced Fermi condensates in one dimension Masaki Tezuka and Masahito Ueda Relaxation dynamics in the gapped XXZ spin-1/2 chain Jorn Mossel and Jean-Sébastien Caux Canonical thermalization Peter Reimann Minimally entangled typical thermal state algorithms E M Stoudenmire and Steven R White Manipulation of the dynamics of many-body systems via quantum control methods Julie Dinerman and Lea F Santos Multimode analysis of non-classical correlations in double-well Bose-Einstein condensates Andrew J Ferris and Matthew J Davis Thermalization in a quasi-one-dimensional ultracold bosonic gas I E Mazets and J Schmiedmayer Two simple systems with cold atoms: quantum chaos tests and non-equilibrium dynamics Cavan Stone, Yassine Ait El Aoud, Vladimir A Yurovsky and Maxim Olshanii On the speed of fluctuations around thermodynamic equilibrium Noah Linden, Sandu Popescu, Anthony J Short and Andreas Winter A quantum central limit theorem for non-equilibrium systems: exact local relaxation of correlated states M Cramer and J Eisert Quantum quench dynamics of the sine-Gordon model in some solvable limits A Iucci and M A Cazalilla Nonequilibrium quantum dynamics of atomic dark solitons A D Martin and J Ruostekoski Quantum quenches in the anisotropic spin-1?2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler and Ehud Altman Crossover from adiabatic to sudden interaction quenches in the Hubbard model: prethermalization and non-equilibrium dynamics Mic
Nonlocality in many-body quantum systems detected with two-body correlators
J. Tura; R. Augusiak; A. B. Sainz; B. Lücke; C. Klempt; M. Lewenstein; A. Acín
2015-05-25
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states---ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
Isolated many-body quantum systems far from equilibrium: Relaxation process and thermalization
Torres-Herrera, E. J.; Santos, Lea F.
2014-10-15
We present an overview of our recent numerical and analytical results on the dynamics of isolated interacting quantum systems that are taken far from equilibrium by an abrupt perturbation. The studies are carried out on one-dimensional systems of spins-1/2, which are paradigmatic models of many-body quantum systems. Our results show the role of the interplay between the initial state and the post-perturbation Hamiltonian in the relaxation process, the size of the fluctuations after equilibration, and the viability of thermalization.
Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System
C. Senko; J. Smith; P. Richerme; A. Lee; W. C. Campbell; C. Monroe
2014-01-22
Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the results of such simulations will also become classically intractable as system sizes increase. In this work, we introduce and implement a coherent imaging spectroscopic technique to validate a quantum simulation, much as magnetic resonance imaging exposes structure in condensed matter. We use this method to determine the energy levels and interaction strengths of a fully-connected quantum many-body system. Additionally, we directly measure the size of the critical energy gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators once experiments advance beyond proof-of-principle demonstrations and exceed the resources of conventional computers.
Fluctuations and Stochastic Processes in One-Dimensional Many-Body Quantum Systems
Stimming, H.-P.; Mauser, N. J. [Wolfgang Pauli Institute c/o Universitaet Wien, Nordbergstrasse 15, 1090 Vienna (Austria); Schmiedmayer, J. [Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna (Austria); Mazets, I. E. [Wolfgang Pauli Institute c/o Universitaet Wien, Nordbergstrasse 15, 1090 Vienna (Austria); Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna (Austria); Ioffe Physico-Technical Institute, 194021 St. Petersburg (Russian Federation)
2010-07-02
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter, we develop a semiclassical description of the fluctuation properties based on the Ornstein-Uhlenbeck stochastic process. As an illustration, we analyze the phase correlation functions and the full statistical distributions of the interference between two one-dimensional systems, either independent or tunnel-coupled, and compare with the Luttinger-liquid theory.
Tomotaka Kuwahara; Takashi Mori; Keiji Saito
2015-08-24
We consider the effective Floquet Hamiltonian for a wide range of many-body quantum systems under periodic driving. The Floquet-Magnus (FM) expansion is known to have a formal expression of the Floquet Hamiltonian. However, this series expansion is in general divergent in the thermodynamic limit. We rigorously show that a truncated version of the FM expansion accurately describes transient dynamics for a wide range of Hamiltonian systems. This optimal expression reveals several universal properties of transient quantum dynamics. We show the connection of our findings with several dynamical phenomena such as dynamical localization and thermalization, and so on.
Thermopower as a tool to investigate many-body effects in quantum systems
Kristinsdóttir, L. H.; Bengtsson, J.; Reimann, S. M.; Wacker, A.; Linke, H.
2014-08-25
Measuring the thermopower of a confined quantum system reveals important information about its excitation spectrum. Our simulations show how this kind of transport spectroscopy is able to extract a clear signal for the onset of Wigner localization in a nanowire segment. This demonstrates that thermopower measurements provide a tool for investigating complex many-body quantum effects, which is less intrusive than the usual charge-stability diagram as no high source-drain bias is required. While the effect is most pronounced for weak tunnel coupling and low temperatures, the excited states also significantly affect the thermopower spectrum at moderate temperature, adding distinct features to the characteristic thermopower lineshape.
Seniority in quantum many-body systems. I. Identical particles in a single shell
NASA Astrophysics Data System (ADS)
Van Isacker, P.; Heinze, S.
2014-10-01
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of partial conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions.
Simulating local measurements on a quantum many body system with stochastic matrix product states
Søren Gammelmark; Klaus Mølmer
2009-11-25
We demonstrate how to simulate both discrete and continuous stochastic evolution of a quantum many body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators is found. The technique is exemplified by numerical simulations of the anti-ferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular we focus on local measurements with small support and non-local measurements which induces long range correlations.
Extracting signatures of quantum criticality in the finite-temperature behavior of many-body systems
NASA Astrophysics Data System (ADS)
Cuccoli, Alessandro; Taiti, Alessio; Vaia, Ruggero; Verrucchi, Paola
2007-08-01
We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum S=1/2 Ising chain is exactly solvable and extensively studied, results for the classical limit (S??) of such model are lacking, and we supply them here. They are obtained numerically, via the transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to the thermal ones.
NASA Astrophysics Data System (ADS)
Gernoth, K. A.
2010-12-01
A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.
Equivalent dynamical complexity in a many-body quantum and collective human system
Johnson, Neil F; Zhao, Zhenyuan; Quiroga, Luis
2010-01-01
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms [1-7]. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding concerning quantum many-body effects in cuprate superconductors [8,9] (i.e. scale of 10^{-9}-10^{-4} meters and 10^{-12}-10^{-6} seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism [10] (i.e. scale of 10^{3}-10^{6} meters and 10^{4}-10^{8} seconds), (iii) shows consistency with var...
NASA Astrophysics Data System (ADS)
Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin
2015-03-01
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1–J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.
Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin
2015-03-01
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results. PMID:25654245
Lieb-Robinson Bounds and Quasi-locality for the Dynamics of Many-Body Quantum Systems
Robert Sims
2010-11-20
We review a recently proven Lieb-Robinson bound for general, many-body quantum systems with bounded interactions. Several basic examples are discussed as well as the connection between commutator estimates and quasi-locality.
Local convertibility and the quantum simulation of edge states in many-body systems
Fabio Franchini; Jian Cui; Luigi Amico; Heng Fan; Mile Gu; Vladimir E. Korepin; Leong Chuan Kwek; Vlatko Vedral
2014-09-23
In some many-body systems, certain ground state entanglement (Renyi) entropies increase even as the correlation length decreases. This entanglement non-monotonicity is a potential indicator of non-classicality. In this work we demonstrate that such a phenomenon, known as non-local convertibility, is due to the edge state (de)construction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transitions. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions (A|B) and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show non-local convertibility if either A or B are smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry breaking) ground state is always locally convertible. The edge states behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and non-local, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Spectrum of quantum transfer matrices via classical many-body systems
NASA Astrophysics Data System (ADS)
Gorsky, A.; Zabrodin, A.; Zotov, A.
2014-01-01
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous n -invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N -body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N -dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the n Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.
Energy as an entanglement witness for quantum many-body systems
Dowling, Mark R.; Doherty, Andrew C.; Bartlett, Stephen D. [School of Physical Sciences, University of Queensland, Queensland 4072 (Australia)
2004-12-01
We investigate quantum many-body systems where all low-energy states are entangled. As a tool for quantifying such systems, we introduce the concept of the entanglement gap, which is the difference in energy between the ground-state energy and the minimum energy that a separable (unentangled) state may attain. If the energy of the system lies within the entanglement gap, the state of the system is guaranteed to be entangled. We find Hamiltonians that have the largest possible entanglement gap; for a system consisting of two interacting spin-1/2 subsystems, the Heisenberg antiferromagnet is one such example. We also introduce a related concept, the entanglement-gap temperature: the temperature below which the thermal state is certainly entangled, as witnessed by its energy. We give an example of a bipartite Hamiltonian with an arbitrarily high entanglement-gap temperature for fixed total energy range. For bipartite spin lattices we prove a theorem demonstrating that the entanglement gap necessarily decreases as the coordination number is increased. We investigate frustrated lattices and quantum phase transitions as physical phenomena that affect the entanglement gap.
Bei Zeng; Xie Chen; Duan-Lu Zhou; Xiao-Gang Wen
2015-08-11
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.
Bei Zeng; Xie Chen; Duan-Lu Zhou; Xiao-Gang Wen
2015-09-21
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.
Lattice mapping for many-body open quantum systems and its application to atoms in photonic cystals
Ines de Vega
2014-10-17
We present a derivation that maps the original problem of a many body open quantum system (OQS) coupled to a harmonic oscillator reservoir into that of a many body OQS coupled to a lattice of harmonic oscillators. The present method is particularly suitable to analyse the dynamics of atoms arranged in a periodic structure and coupled the EM field within a photonic crystal. It allows to solve the dynamics of a many body OQS with methods alternative to the commonly used master, stochastic Schr\\"{o}dinger and Heisenberg equations, and thus to reach regimes well beyond the weak coupling and Born-Markov approximations.
Trugman, S.A.
1989-01-01
The problem of how to visualize and sometimes solve a general many-body system is considered. The ideas are established in the context of very simple small systems, a Hubbard model and a coupled electron-phonon model, both on two lattice sites. These models are also solved to good approximation in the thermodynamic limit, although the Hubbard model is restricted to a small number of holes away from the Mott insulating state. Response functions are also considered. A fairly general many-body Hamiltonian is considered. It consists of an electron or other fermion kinetic energy and electron-electron interactions, which may be coupled to a bose field such as a phonon. The phonons themselves may be nonlinear (have self-interactions). The system may be strongly coupled. One may also add coupling to an external driving field, such as an ac electric field. The methods discussed are nonperturbative, and so differ from the standard methods of diagrammatic perturbation theory. A comparison is made with diagrammatic methods in the context of the random phase approximation. 6 refs., 12 figs.
Akinori Nishino; Takashi Imamura; Naomichi Hatano
2009-10-30
We obtain an exact many-body scattering eigenstate in an open quantum dot system. The scattering state is not in the form of the Bethe eigenstate in the sense that the wave-number set of the incoming plane wave is not conserved during the scattering and many-body bound states appear. By using the scattering state, we study the average nonequilibrium current through the quantum dot under a finite bias voltage. The current-voltage characteristics that we obtained by taking the two-body bound state into account is qualitatively similar to several known results.
Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System
NASA Astrophysics Data System (ADS)
Smith, Jacob; Senko, Crystal; Richerme, Phil; Lee, Aaron; Campbell, Wes; Monroe, Chris
2014-05-01
Trapped-ion quantum simulators are a promising candidate for exploring quantum-many-body physics, such as quantum magnetism, that are difficult to examine in condensed-matter experiments or using classical simulation. We demonstrate a coherent imaging spectroscopic technique to validate a quantum simulation. In this work, we study fully-connected transverse Ising models with a chain of up to 18 171Yb+ ions. Here, We resolve the state of each spin by collecting the spin-dependent fluorescence on a camera in order to map the complete energy spectrum and fully characterize the spin-spin couplings, while also engineering entangled states and measuring the critical gap near a quantum phase transition. We expect this general technique to become an important verification tool for quantum simulators. This work is supported by grants from the U.S. Army Research Office with funding from the DARPA OLE program, IARPA, and the MURI program; and the NSF Physics Frontier Center at JQI.
A link of information entropy and kinetic energy for quantum many-body systems
Massen, S E
2001-01-01
A direct connection of information entropy $S$ and kinetic energy $T$ is obtained for nuclei and atomic clusters, which establishes $T$ as a measure of the information in a distribution. It is conjectured that this is a universal property for fermionic many-body systems. We also check rigorous inequalities previously found to hold between S and T for atoms and verify that they hold for nuclei and atomic clusters as well. These inequalities give a relationship of Shannon's information entropy in position-space with an experimental quantity i.e. the rms radius of nuclei and clusters.
A geometrical approach to the mean density of states in many-body quantum systems
Quirin Hummel; Juan Diego Urbina; Klaus Richter
2012-10-21
We present a novel analytical approach for the calculation of the mean density of states in many-body systems made of confined indistinguishable and non-interacting particles. Our method makes explicit the intrinsic geometry inherent in the symmetrization postulate and, in the spirit of the usual Weyl expansion for the smooth part of the density of states in single-particle confined systems, our results take the form of a sum over clusters of particles moving freely around manifolds in configuration space invariant under elements of the group of permutations. Being asymptotic, our approximation gives increasingly better results for large excitation energies and we formally confirm that it coincides with the celebrated Bethe estimate in the appropriate region. Moreover, our construction gives the correct high energy asymptotics expected from general considerations, and shows that the emergence of the fermionic ground state is actually a consequence of an extremely delicate large cancellation effect. Remarkably, our expansion in cluster zones is naturally incorporated for systems of interacting particles, opening the road to address the fundamental problem about the interplay between confinement and interactions in many-body systems of identical particles.
Thomas Chung; Stephen D. Bartlett; Andrew C. Doherty
2009-04-17
In measurement-based quantum computation (MBQC), local adaptive measurements are performed on the quantum state of a lattice of qubits. Quantum gates are associated with a particular measurement sequence, and one way of viewing MBQC is that such a measurement sequence prepares a resource state suitable for `gate teleportation'. We demonstrate how to quantify the performance of quantum gates in MBQC by using correlation functions on the pre-measurement resource state.
A Correlation Estimate for Quantum Many-Body Systems at Positive Temperature
Robert Seiringer
2006-04-18
We present an inequality that gives a lower bound on the expectation value of certain two-body interaction potentials in a general state on Fock space in terms of the corresponding expectation value for thermal equilibrium states of non-interacting systems and the difference in the free energy. This bound can be viewed as a rigorous version of first order perturbation theory for many-body systems at positive temperature. As an application, we give a proof of the first two terms in a high density (and high temperature) expansion of the free energy of jellium with Coulomb interactions, both in the fermionic and bosonic case. For bosons, our method works above the transition temperature (for the non-interacting gas) for Bose-Einstein condensation.
Hofmann, C S; Schempp, H; Müller, N L M; Faber, A; Busche, H; Robert-de-Saint-Vincent, M; Whitlock, S; Weidemüller, M
2013-01-01
Recent developments in the study of ultracold Rydberg gases demand an advanced level of experimental sophistication, in which high atomic and optical densities must be combined with excellent control of external fields and sensitive Rydberg atom detection. We describe a tailored experimental system used to produce and study Rydberg-interacting atoms excited from dense ultracold atomic gases. The experiment has been optimized for fast duty cycles using a high flux cold atom source and a three beam optical dipole trap. The latter enables tuning of the atomic density and temperature over several orders of magnitude, all the way to the Bose-Einstein condensation transition. An electrode structure surrounding the atoms allows for precise control over electric fields and single-particle sensitive field ionization detection of Rydberg atoms. We review two experiments which highlight the influence of strong Rydberg--Rydberg interactions on different many-body systems. First, the Rydberg blockade effect is used to pre...
Olmos, Beatriz; Lesanovsky, Igor; Garrahan, Juan P
2014-10-01
We explore the relaxation dynamics of quantum many-body systems that undergo purely dissipative dynamics through non-classical jump operators that can establish quantum coherence. Our goal is to shed light on the differences in the relaxation dynamics that arise in comparison to systems evolving via classical rate equations. In particular, we focus on a scenario where both quantum and classical dissipative evolution lead to a stationary state with the same values of diagonal or "classical" observables. As a basis for illustrating our ideas we use spin systems whose dynamics becomes correlated and complex due to dynamical constraints, inspired by kinetically constrained models (KCMs) of classical glasses. We show that in the quantum case the relaxation can be orders of magnitude slower than the classical one due to the presence of quantum coherences. Aspects of these idealized quantum KCMs become manifest in a strongly interacting Rydberg gas under electromagnetically induced transparency (EIT) conditions in an appropriate limit. Beyond revealing a link between this Rydberg gas and the rather abstract dissipative KCMs of quantum glassy systems, our study sheds light on the limitations of the use of classical rate equations for capturing the non-equilibrium behavior of this many-body system. PMID:25375478
M. Cianciaruso; S. M. Giampaolo; W. Roga; G. Zonzo; M. Blasone; F. Illuminati
2014-12-02
Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum systems. The distance between a given state and its image under least perturbing local unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, for pure states, while for mixed states it is a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unifying approach, we perform a detailed comparison between two-body entanglement and two-body quantum correlations in infinite XY quantum spin chains both in symmetry-preserving and symmetry-breaking ground states as well as in thermal states at finite temperature.
J. Barea; R. Bijker; A. Frank
2009-04-16
The observed preponderance of ground states with angular momentum L=0 in many-body quantum systems with random two-body interactions is analyzed in terms of correlation coefficients (covariances) among different eigenstates. It is shown that the geometric analysis of Chau {\\it et al.} can be interpreted in terms of correlations (covariances) between energy eigenvalues thus providing an entirely statistical explanation of the distribution of ground state angular momenta of randomly interacting quantum systems which, in principle, is valid for both fermionic and bosonic systems. The method is illustrated for the interacting boson model.
NASA Astrophysics Data System (ADS)
Deckman, Jason
The following dissertation is an account of my research in the Mandelshtam group at UC Irvine beginning in the Fall of 2006 and ending in the Summer of 2011. My general area of study falls within the realm of equilibrium quantum statistical mechanics, a discipline which attempts to relate molecular-scale properties to time averaged, macroscopic observables. The major tools used herein are the Variational Gaussian Wavepacket (VGW) approximation for quantum calculations, and Monte-Carlo methods, particularly parallel tempering, for global optimization and the prediction of equilibrium thermodynamic properties. Much of my work used these two methods to model both small and bulk systems at equilibrium where quantum effects are significant. All the systems considered are characterized by inter-molecular van der Waals forces, which are weak but significant electrostatic attractions between atoms and molecules and posses a 1/r6 dependence. The research herein begins at the microscopic level, starting with Lennard-Jones (LJ) clusters, then later shifts to the macroscopic for a study involving bulk para-hydrogen. For the LJ clusters the structural transitions induced by a changing deBoer parameter, ?, a measure of quantum delocalization of the constituent particles, are investigated over a range of cluster sizes, N. From the data a "phase" diagram as a function of ? and N is constructed, which depicts the structural motifs favored at different size and quantum parameter. Comparisons of the "quantum induced" structural transitions depicted in the latter are also made with temperature induced transitions and those caused by varying the range of the Morse potential. Following this, the structural properties of binary para-Hydrogen/ ortho-Deuterium clusters are investigated using the VGW approximation and Monte-Carlo methods within the GMIN framework. The latter uses the "Basin-Hopping" algorithm, which simplifies the potential energy landscape, and coupled with the VGW approximation, an efficient and viable method for predicting equilibrium quantum mechanical properties is demonstrated. In the next chapter my contribution to the numerical implementation of the Thermal Gaussian Molecular Dynamics (TGMD) method is discussed. Within TGMD, a mapping of a quantum system to a classical is performed by means of an effective Hamiltonian, H eff, which is computed within the VGW framework. Using the classical dynamical equations of motion with Heff, the properties of a quantum system can be modeled within a classical framework. After this, the bulk system of fluid para-Hydrogen is investigated using the VGW in the NPT ensemble in an attempt to derive the thermodynamic properties at the phase transition and construct the equation of state. The dissertation then concludes with a discussion on the adaptation of the VGW methodology to any molecular system.
Macroscopic quantum superpositions in highly-excited strongly-interacting many-body systems
S. Yu. Kun; L. Benet; L. T. Chadderton; W. Greiner; F. Haas
2003-02-05
We demonstrate a break-down in the macroscopic (classical-like) dynamics of wave-packets in complex microscopic and mesoscopic collisions. This break-down manifests itself in coherent superpositions of the rotating clockwise and anticlockwise wave-packets in the regime of strongly overlapping many-body resonances of the highly-excited intermediate complex. These superpositions involve $\\sim 10^4$ many-body configurations so that their internal interactive complexity dramatically exceeds all of those previously discussed and experimentally realized. The interference fringes persist over a time-interval much longer than the energy relaxation-redistribution time due to the anomalously slow phase randomization (dephasing). Experimental verification of the effect is proposed.
NASA Astrophysics Data System (ADS)
Lavalle, Catia; Rigol, Marcos; Muramatsu, Alejandro
2005-08-01
The cover picture of the current issue, taken from the Feature Article [1], depicts the evolution of local density (a) and its quantum fluctuations (b) in trapped fermions on one-dimensional optical lattices. As the number of fermions in the trap is increased, figure (a) shows the formation of a Mott-insulating plateau (local density equal to one) whereas the quantum fluctuations - see figure (b) - are strongly suppressed, but nonzero. For a larger number of fermions new insulating plateaus appear (this time with local density equal to two), but no density fluctuations. Regions with non-constant density are metallic and exhibit large quantum fluctuations of the density.The first author Catia Lavalle is a Postdoc at the University of Stuttgart. She works in the field of strongly correlated quantum systems by means of Quantum Monte Carlo methods (QMC). While working on her PhD thesis at the University of Stuttgart, she developed a new QMC technique that allows to study dynamical properties of the t-J model.
NASA Astrophysics Data System (ADS)
Veits, Oliver; Fleischhauer, Michael
1997-04-01
We analyze the influence of system-size effects on the quantum properties of a degenerate parametric oscillator below, at, and above the classical threshold using a Green's-function approach. The many-body technique permits a systematic analysis of finite-size corrections to standard linearization results. In particular we study a ``semiquantum'' limit, where even above threshold only few photons are in the subharmonic mode while the pump mode is highly populated and behaves quasiclassically. Substantial deviations from classical and linearization predictions are found. We show that the depletion of the pump mode is rather strong and the threshold of parametric oscillation is shifted to higher pump strength, when the subharmonic system is small.
Many Body Symmetrical Dynamical Systems
Muhammad Shoaib
2007-09-05
We investigate the stability of few body symmetrical dynamical systems which include four and five body symmetrical dynamical systems. Research presented in this thesis includes the following original investigations: determination of some analytical solutions of the four body problem; stability analysis of the near symmetric coplanar CSFBP ; derivation of the analytical stability criterion valid for all time for a special symmetric configuration of the general five-body problem, the CS5BP, which exhibits many of the salient characteristics of the general five body problem; numerical investigation of the hierarchical stability of the CS5BP and derivation of the stability criterion for the CSNBP.
Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems
NASA Astrophysics Data System (ADS)
Dukelsky, J.; Pittel, S.; Sierra, G.
2004-07-01
The use of exactly solvable Richardson-Gaudin models to describe the physics of systems with strong pair correlations is reviewed. The article begins with a brief discussion of Richardson’s early work, which demonstrated the exact solvability of the pure pairing model, and then shows how that work has evolved recently into a much richer class of exactly solvable models. The Richardson solution leads naturally to an exact analogy between these quantum models and classical electrostatic problems in two dimensions. This analogy is then used to demonstrate formally how BCS theory emerges as the large- N limit of the pure pairing Hamiltonian. Several applications to problems of relevance to condensed-matter physics, nuclear physics, and the physics of confined systems are considered. Some of the interesting effects that are discussed in the context of these exactly solvable models include (i) the crossover from superconductivity to a fluctuation-dominated regime in small metallic grains; (ii) the role of the nucleon Pauli principle in suppressing the effects of high-spin bosons in interacting boson models of nuclei, and (iii) the possibility of fragmentation in confined boson systems. Interesting insight is also provided into the origin of the superconducting phase transition both in two-dimensional electronic systems and in atomic nuclei, based on the electrostatic image of the corresponding exactly solvable quantum pairing models.
Quantum Field Theory of Many-body Systems from the Origin of Sound
Wen, Xiao-Gang
and fractional statistics, quantum Hall effects, topological/quantum order, spin liquid and string, spin liquid, string-net condensation, quantum Hall effect, path integral, effective field theory 1, effective theory, origin of light, origin of electron, topological order, quantum order, ether 2. Path
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
Stefano Iubini; Octavi Boada; Yasser Omar; Francesco Piazza
2015-05-13
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local vs non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Many-body entanglement in gapped quantum systems : representation, classification, and application
Chen, Xie, Ph. D. Massachusetts Institute of Technology
2012-01-01
Entanglement is a special form of quantum correlation that exists among quantum particles and it has been realized that surprising things can happen when a large number of particles are entangled together. For example, ...
Controlling the dynamics of an open many-body quantum system with localized dissipation
G. Barontini; R. Labouvie; F. Stubenrauch; A. Vogler; V. Guarrera; H. Ott
2012-12-19
We experimentally investigate the action of a localized dissipative potential on a macroscopic matter wave, which we implement by shining an electron beam on an atomic Bose-Einstein condensate (BEC). We measure the losses induced by the dissipative potential as a function of the dissipation strength observing a paradoxical behavior when the strength of the dissipation exceeds a critical limit: for an increase of the dissipation rate the number of atoms lost from the BEC becomes lower. We repeat the experiment for different parameters of the electron beam and we compare our results with a simple theoretical model, finding excellent agreement. By monitoring the dynamics induced by the dissipative defect we identify the mechanisms which are responsible for the observed paradoxical behavior. We finally demonstrate the link between our dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect. Due to the high degree of control on every parameter, our system is a promising candidate for the engineering of fully governable open quantum systems.
C. Eichler; J. Mlynek; J. Butscher; P. Kurpiers; K. Hammerer; T. J. Osborne; A. Wallraff
2015-08-26
Improving the understanding of strongly correlated quantum many body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate and experimentally probe the properties of such systems. In this work we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product states - a class of states which has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics (cQED) system we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to exotic models involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.
Probing quantum and thermal noise in an interacting many-body system
Loss, Daniel
Physik, Universit¨at Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria 5 Department of Physics statistics in an atom laser11 and the Hanbury BrownTwiss effect for both bosons and fermions12KosterlitzThouless transition in a two-dimensional quantum gas16 . Recently, it has been suggested that the full statistics
Berry's phase in a one-dimensional quantum many-body system
Schuetz, G. (Department of Physics, Weizmann Institute, Rehovot 76100 (Israel))
1994-03-01
We study an interacting one-dimensional quantum lattice gas of massive fermions on a ring with [ital L] lattice sites. The ring is threaded by a magnetic flux corresponding to a twist in boundary conditions. We compute the periodicity of the ground state under an adiabatically increasing flux and the associated Berry's phase occurring in this process. The model has a second-order phase transition line which coincides with a line where the Berry phase changes nonanalytically.
PHYSICAL REVIEW B 91, 184202 (2015) Dynamics in many-body localized quantum systems without disorder
Müller, Markus
2015-01-01
by an incomplete volume-law entanglement, could exist in systems without disorder. Such an interaction of interest to us classical frustration plays no role, in contrast to systems that inherit their nonergodicity
Many-body localization in the quantum random energy model
NASA Astrophysics Data System (ADS)
Laumann, Chris; Pal, Arijeet
2014-03-01
The quantum random energy model is a canonical toy model for a quantum spin glass with a well known phase diagram. We show that the model exhibits a many-body localization-delocalization transition at finite energy density which significantly alters the interpretation of the statistical ``frozen'' phase at lower temperature in isolated quantum systems. The transition manifests in many-body level statistics as well as the long time dynamics of on-site observables. CRL thanks the Perimeter Institute for hospitality and support.
Decoherence of many-body systems due to many-body interactions
T. Carle; H. J. Briegel; B. Kraus
2010-07-30
We study a spin-gas model, where N_S system qubits are interacting with N_B bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decohenerce induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between baths that are coupled to different individual system qubit and compare Markovian with non-Markovian interactions. As examples we consider specific quantum many-body states and investigate their evolution under several different decoherence models. As a complementary investigation we study how the coupling to the environment can be employed to generate a desired multipartite state.
Lao, Ka Un; Herbert, John M
2015-01-15
We present an overview of "XSAPT", a family of quantum chemistry methods for noncovalent interactions. These methods combine an efficient, iterative, monomer-based approach to computing many-body polarization interactions with a two-body version of symmetry-adapted perturbation theory (SAPT). The result is an efficient method for computing accurate intermolecular interaction energies in large noncovalent assemblies such as molecular and ionic clusters, molecular crystals, clathrates, or protein-ligand complexes. As in traditional SAPT, the XSAPT energy is decomposable into physically meaningful components. Dispersion interactions are problematic in traditional low-order SAPT, and two new approaches are introduced here in an attempt to improve this situation: (1) third-generation empirical atom-atom dispersion potentials, and (2) an empirically scaled version of second-order SAPT dispersion. Comparison to high-level ab initio benchmarks for dimers, water clusters, halide-water clusters, a methane clathrate hydrate, and a DNA intercalation complex illustrate both the accuracy of XSAPT-based methods as well as their limitations. The computational cost of XSAPT scales as O(N(3))-O(N(5)) with respect to monomer size, N, depending upon the particular version that is employed, but the accuracy is typically superior to alternative ab initio methods with similar scaling. Moreover, the monomer-based nature of XSAPT calculations makes them trivially parallelizable, such that wall times scale linearly with respect to the number of monomer units. XSAPT-based methods thus open the door to both qualitative and quantitative studies of noncovalent interactions in clusters, biomolecules, and condensed-phase systems. PMID:25408114
Many-Body Localization in Dipolar Systems
NASA Astrophysics Data System (ADS)
Yao, N. Y.; Laumann, C. R.; Gopalakrishnan, S.; Knap, M.; Müller, M.; Demler, E. A.; Lukin, M. D.
2014-12-01
Systems of strongly interacting dipoles offer an attractive platform to study many-body localized phases, owing to their long coherence times and strong interactions. We explore conditions under which such localized phases persist in the presence of power-law interactions and supplement our analytic treatment with numerical evidence of localized states in one dimension. We propose and analyze several experimental systems that can be used to observe and probe such states, including ultracold polar molecules and solid-state magnetic spin impurities.
Chapman, Michael
. The spinor Bose-Einstein condensate is initialized to an unstable fixed point of the spin-nematic phase space-dependent [21] interaction strength and by time varying the trapping potential in a double-well Bose dynamic stabilization of a strongly interacting quantum many-body spin system by periodic manipulation
Benet, L. [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (UNAM), 62210-Cuernavaca, Morelos (Mexico); Chadderton, L. T. [Atomic and Molecular Physics Laboratary, RSPhysSE, Australian National University, Canberra ACT 0200 (Australia); Kun, S. Yu. [Facultad de Ciencias, Universidad Autonoma del Estado de Morelos (UAEM), 62209-Cuernavaca, Morelos (Mexico); Nonlinear Physics Center and Department of Theoretical Physics, RSPhysSE, Australian National University, Canberra ACT 0200 (Australia); Qi Wang [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China)
2007-06-15
We study coherent superpositions of clockwise and anticlockwise rotating intermediate complexes with overlapping resonances formed in bimolecular chemical reactions. Disintegration of such complexes represents an analog of a famous double-slit experiment. The time for disappearance of the interference fringes is estimated from heuristic arguments related to fingerprints of chaotic dynamics of a classical counterpart of the coherently rotating complex. Validity of this estimate is confirmed numerically for the H+D{sub 2} chemical reaction. Thus we demonstrate the quantum-classical transition in temporal behavior of highly excited quantum many-body systems in the absence of external noise and coupling to an environment.
Entanglement and Nonlocality in Many-Body Systems: a primer
J. Tura; A. B. Sainz; T. Grass; R. Augusiak; A. Acín; M. Lewenstein
2015-01-12
Current understanding of correlations and quantum phase transitions in many-body systems has significantly improved thanks to the recent intensive studies of their entanglement properties. In contrast, much less is known about the role of quantum non-locality in these systems. On the one hand, standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. On the other hand, most of the available multipartite Bell inequalities involve correlations among many particles. Such correlations are notoriously hard to access theoretically, and even harder experimentally. Typically, there is no Bell inequality for many-body systems built only from low-order correlation functions. Recently, however, it has been shown in [J. Tura et al., Science 344, 1256 (2014)] that multipartite Bell inequalities constructed only from two-body correlation functions are strong enough to reveal non-locality in some many-body states, in particular those relevant for nuclear and atomic physics. The purpose of this lecture is to provide an overview of the problem of quantum correlations in many-body systems - from entanglement to nonlocality - and the methods for their characterization.
Estimation of many-body quantum Hamiltonians via compressive sensing
Shabani, A.
We develop an efficient and robust approach for quantum measurement of nearly sparse many-body quantum Hamiltonians based on the method of compressive sensing. This work demonstrates that with only O(sln(d)) experimental ...
Marc Bienert; Jorge Flores; Sergey Yu. Kun
2006-06-07
We estimate how accurate the phase relaxation time of quantum many-body systems can be determined from data on forward peaking of evaporating protons from a compound nucleus. The angular range and accuracy of the data needed for a reliable determination of the phase relaxation time are evaluated. The general method is applied to analyze the inelastic scattering of 18 MeV protons from Pt for which previously measured double differential cross sections for two angles in the evaporating domain of the spectra show a strong forward peaking. A new experiment for an improved determination of the phase relaxation time is proposed. The experiment is also highly desirable for an accurate test of a formation of thermalized non-equilibrated matter in quantum many-body systems.
Piotr Piecuch
1989-01-01
In the previous papers of this series we have given a complete classification and analytical description of all possible types of long-range intermolecular forces in an arbitrary molecular system including quantum-mechanical many-body effects that are predicted by the first three orders of the Rayleigh-Schrödinger perturbation theory accompanied by a multipole approximation. The final anisotropic and isotropic interaction energy expressions possess
Quantum many-body fluctuations around nonlinear Schrödinger dynamics
Chiara Boccato; Serena Cenatiempo; Benjamin Schlein
2015-09-13
We consider the many body quantum dynamics of systems of bosons interacting through a two-body potential $N^{3\\beta-1} V (N^\\beta x)$, scaling with the number of particles $N$. For $0< \\beta < 1$, we obtain a norm-approximation of the evolution of an appropriate class of data on the Fock space. To this end, we need to correct the evolution of the condensate described by the one-particle nonlinear Schr\\"odinger equation by means of a fluctuation dynamics, governed by a quadratic generator.
Exploring flocking via quantum many-body physics techniques
NASA Astrophysics Data System (ADS)
Souslov, Anton; Loewe, Benjamin; Goldbart, Paul M.
2015-03-01
Flocking refers to the spontaneous breaking of spatial isotropy and time-reversal symmetries in collections of bodies such as birds, fish, locusts, bacteria, and artificial active systems. The transport of matter along biopolymers using molecular motors also involves the breaking of these symmetries, which in some cases are known to be broken explicitly. We study these classical nonequilibrium symmetry-breaking phenomena by means of models of many strongly interacting particles that hop on a periodic lattice. We employ a mapping between the classical and quantum dynamics of many-body systems, combined with tools from many-body theory. In particular, we examine the formation and properties of nematic and polar order in low-dimensional, strongly-interacting active systems using techniques familiar from fermionic systems, such as self-consistent field theory and bosonization. Thus, we find that classical active systems can exhibit analogs of quantum phenomena such as spin-orbit coupling, magnetism, and superconductivity. The models we study connect the physics of asymmetric exclusion processes to the spontaneous emergence of transport and flow, and also provide a soluble cousin of Vicsek's model system of self-propelled particles.
Comment on 'Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined'
Rigol, Marcos [Department of Physics, Georgetown University, Washington, DC 20057 (United States)
2010-09-15
In a recent paper, Roux [Phys. Rev. A 79, 021608(R) (2009)] argued that thermalization in a Bose-Hubbard system, after a quantum quench, follows from the approximate Boltzmann distribution of the overlap between the initial state and the eigenstates of the final Hamiltonian. We show here that the distribution of the overlaps is in general not related to the canonical (or microcanonical) distribution and, hence, it cannot explain why thermalization occurs in quantum systems.
Planar limit of 1D many-body system
Zuo, Fen
2015-01-01
We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one dimensional interacting many-body system can be solved exactly when the particle number goes to infinity. As an example, bosonic and two-component fermionic systems with a $\\delta$-function interaction are analyzed in detail.
Invariant manifolds and collective motion in many-body systems
T. Papenbrock; T. H. Seligman
2002-06-21
Collective modes of interacting many-body systems can be related to the motion on classically invariant manifolds. We introduce suitable coordinate systems. These coordinates are Cartesian in position and momentum space. They are collective since several components vanish for motion on the invariant manifold. We make a connection to Zickendraht's collective coordinates and also obtain shear modes. The importance of collective configurations depends on the stability of the manifold. We present an example of quantum collective motion on the manifold
Collision Microscope to Study Many-Body Quantum Entanglement
NASA Astrophysics Data System (ADS)
Price, Craig; Liu, Qi; Gemelke, Nathan
2014-05-01
Quantum entanglement over long length scales is present in both quantum critical and quantum ordered many-body systems and can often be used as a fingerprint for underlying dynamics or ground-state structure. Limited quantum measurement and thermal back-action via controlled collisions of cold atoms and subsequent optical detection can be used to probe long-range entanglement. Entanglement Entropy has recently arisen as a quantitative vehicle to describe entanglement in thermodynamic systems, and its scaling with area can reveal detailed character of the system. We present progress in constructing an apparatus to experimentally extract Entanglement Entropy through pair-wise entanglement of cold fermionic potassium and bosonic cesium gases. The measurement will be made by translating localized probe atoms through a portion of a strongly entangled sample, then recording the heating effect of back-action after optical detection of probe atoms. To do so, precise independent control over the atoms will be maintained in a bichromatic lattice formed with a monolithic, common-mode optical setup imbedded in a quantum gas microscope. Other applications are discussed, including cooling of a Mott-Insulator and study of non-equilibrium quantum systems.
NASA Astrophysics Data System (ADS)
Bonitz, M.; Hermanns, S.; Kobusch, K.; Balzer, K.
2013-03-01
The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green functions—the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane—for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.
Quantum many-body dynamics in optomechanical arrays.
Ludwig, Max; Marquardt, Florian
2013-08-16
We study the nonlinear driven dissipative quantum dynamics of an array of optomechanical systems. At each site of such an array, a localized mechanical mode interacts with a laser-driven cavity mode via radiation pressure, and both photons and phonons can hop between neighboring sites. The competition between coherent interaction and dissipation gives rise to a rich phase diagram characterizing the optical and mechanical many-body states. For weak intercellular coupling, the mechanical motion at different sites is incoherent due to the influence of quantum noise. When increasing the coupling strength, however, we observe a transition towards a regime of phase-coherent mechanical oscillations. We employ a Gutzwiller ansatz as well as semiclassical Langevin equations on finite lattices, and we propose a realistic experimental implementation in optomechanical crystals. PMID:23992065
Studying many-body physics through quantum coding theory
Yoshida, Beni
2012-01-01
The emerging closeness between correlated spin systems and error-correcting codes enables us to use coding theoretical techniques to study physical properties of many-body spin systems. This thesis illustrates the use of ...
Entanglement replication in driven-dissipative many body systems
S. Zippilli; M. Paternostro; G. Adesso; F. Illuminati
2013-01-13
We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks.
Many body shakeup in quantum well luminescence spectra
NASA Astrophysics Data System (ADS)
Nash, K. J.; Skolnick, M. S.; Saker, M. K.; Bass, S. J.
1993-05-01
The observation of many body shakeup in the photoluminescence spectra of InGaAs-InP quantum wells, in the quantum Hall regime, is reported. The occurrence of this many body effect is demonstrated from the observation of low energy satellites, corresponding to inter-Landau-level excitations of the degenerate electron gas. Comparison of the zero and finite magnetic field spectra shows that the low energy tail at B=0 also arises from Fermi sea shakeup. The strength of the shakeup is controlled by the localization of the recombining hole, in agreement with recent theoretical predictions.
Jens Hammerling; Boris Gutkin; Thomas Guhr
2009-11-13
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.
Quantum many body physics in single and bilayer graphene
Nandkishore, Rahul (Rahul Mahajan )
2012-01-01
Two dimensional electron systems (2DES) provide a uniquely promising avenue for investigation of many body physics. Graphene constitutes a new and unusual 2DES, which may give rise to unexpected collective phenomena. ...
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Scott Bogner; Aurel Bulgac; Joseph A. Carlson; Jonathan Engel; George Fann; Richard J. Furnstahl; Stefano Gandolfi; Gaute Hagen; Mihai Horoi; Calvin W. Johnson; Markus Kortelainen; Ewing Lusk; Pieter Maris; Hai Ah Nam; Petr Navratil; Witold Nazarewicz; Esmond G. Ng; Gustavo P. A. Nobre; Erich Ormand; Thomas Papenbrock; Junchen Pei; Steven C. Pieper; Sofia Quaglioni; Kenneth J. Roche; Jason Sarich; Nicolas Schunck; Masha Sosonkina; Jun Terasaki; Ian J. Thompson; James P. Vary; Stefan M. Wild
2013-04-12
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; Carlson, Joseph A; Engel, Jonathan; Fann, George; Furnstahl, Richard J; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr; Nazarewicz, Witold; Ng, Esmond G; Nobre, Gustavo P A; Ormand, Erich; Papenbrock, Thomas; Pei, Junchen; Pieper, Steven C; Quaglioni, Sofia; Roche, Kenneth J; Sarich, Jason; Schunck, Nicolas; Sosonkina, Masha; Terasaki, Jun; Thompson, Ian J; Vary, James P; Wild, Stefan M
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Many-body energy localization transition in periodically driven systems
D’Alessio, Luca, E-mail: dalessio@buphy.bu.edu [Physics Department, Boston University, Boston, MA 02215 (United States) [Physics Department, Boston University, Boston, MA 02215 (United States); Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106 (United States); Polkovnikov, Anatoli, E-mail: asp@bu.edu [Physics Department, Boston University, Boston, MA 02215 (United States)] [Physics Department, Boston University, Boston, MA 02215 (United States)
2013-06-15
According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space. -- Highlights: •A dynamical localization transition in periodically driven ergodic systems is found. •This phenomenon is reminiscent of many-body localization in energy space. •Our results are valid for classical and quantum systems in the thermodynamic limit. •At critical frequency, the short time expansion for the evolution operator breaks down. •The transition is associated to a divergent time scale.
Scalapino, D.J.; Sugar, R.L.
1993-12-31
Understanding the physical properties of strongly interacting many-electron systems remains one of the central goals of condensed matter physics. In this project, the authors have developed and implemented numerical techniques, such as quantum Monte Carlo simulations, to study basic models of interacting electrons: the one-band Hubbard model for positive and negative U, the three-band CuO{sub 2} Hubbard model, the Holstein electron-phonon model, the periodic Anderson model, and the Kondo lattice. Such models exhibit a rich variety of physical properties. For example, the half-filled Holstein model undergoes a Peierls-charge-density wave transition. While away from half-filling there is competition between superconductivity and the Peierls-charge-density wave phase. The ground state of the half-filled 2D Hubbard model has long-range antiferromagnetic order. Away from half-filling, it has been found to have an attractive interaction in the singlet d{sub x{sup 2}{minus}y{sup 2}} pairing channel, and it provides a model for the high-temperature cuprate superconductors. Similarly, it is believed that the periodic Anderson model and the Kondo lattice model provide a framework for understanding the heavy fermion materials which can exhibit antiferromagnetic and superconducting phases. Because of the strong coupling and the interplay between the different correlations, it is possible to tip these delicately balanced systems in favor of a given correlated state by the approximations one makes. Thus it is important to develop systematic, controlled calculations for these models. Numerical calculations provide an important approach for determining the properties of such models. A review of the work on these problems is presented.
-modules and spectral analysis of many-body systems
Hilbert C -modules and spectral analysis of many-body systems Mondher DAMAK and Vladimir GEORGESCU. For notations and terminology, see Subsections 2.1, 3.1 and 5.1 1.1 An algebraic approach By many-body system we mean a system of particles interacting between themselves through k-body forces with arbitrary k 1
Two, three, many body systems involving mesons
E. Oset; A. Martinez Torres; K. P. Khemchandani; L. Roca; J. Yamagata
2011-10-31
In this talk we show recent developments on few body systems involving mesons. We report on an approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two body off shell amplitude with three body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off shell part of the amplitudes is most welcome and renders the approach unambiguous, showing that only on shell two body amplitudes need to be used. Within this approach, systems of two mesons and one baryon are studied, reproducing properties of the low lying $1/2^+$ states. On the other hand we also report on multirho and $K^*$ multirho states which can be associated to known meson resonances of high spin.
Jens Hammerling; Boris Gutkin; Thomas Guhr
2010-12-14
We study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction, we calculate the spectral density for collective excitations. We obtain the remarkable result that it always has a unique semiclassical interpretation. We show this by a proper renormalization procedure which allows us to map our system to a Caldeira-Leggett--type of model in which the bath is part of the system.
Derivation of the Cubic Non-linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems
Laszlo Erdos; Benjamin Schlein; Horng-Tzer Yau
2007-02-27
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schr\\"odinger equation in a suitable scaling limit. The result is extended to $k$-particle density matrices for all positive integer $k$.
Many-body localization and quantum ergodicity in disordered long-range Ising models
Philipp Hauke; Markus Heyl
2015-08-30
Ergodicity in quantum many-body systems is - despite its fundamental importance - still an open problem. Many-body localization provides a general framework for quantum ergodicity, and may therefore offer important insights. However, the characterization of many-body localization through simple observables is a difficult task. In this article, we introduce a measure for distances in Hilbert space for spin-1/2 systems that can be interpreted as a generalization of the Anderson localization length to the many-body Hilbert space. We show that this many-body localization length is equivalent to a simple local observable in real space, which can be measured in experiments of superconducting qubits, polar molecules, Rydberg atoms, and trapped ions. Using the many-body localization length and a necessary criterion for ergodicity that it provides, we study many-body localization and quantum ergodicity in power-law-interacting Ising models subject to disorder in the transverse field. Based on the nonequilibrium dynamical renormalization group, numerically exact diagonalization, and an analysis of the statistics of resonances we find a many-body localized phase at infinite temperature for small power-law exponents. Within the applicability of these methods, we find no indications of a delocalization transition.
Many-Body Effects in Quantum-Well Intersubband Transitions
NASA Technical Reports Server (NTRS)
Li, Jian-Zhong; Ning, Cun-Zheng
2003-01-01
Intersubband polarization couples to collective excitations of the interacting electron gas confined in a semiconductor quantum well (Qw) structure. Such excitations include correlated pair excitations (repellons) and intersubband plasmons (ISPs). The oscillator strength of intersubband transitions (ISBTs) strongly varies with QW parameters and electron density because of this coupling. We have developed a set of kinetic equations, termed the intersubband semiconductor Bloch equations (ISBEs), from density matrix theory with the Hartree-Fock approximation, that enables a consistent description of these many-body effects. Using the ISBEs for a two-conduction-subband model, various many-body effects in intersubband transitions are studied in this work. We find interesting spectral changes of intersubband absorption coefficient due to interplay of the Fermi-edge singularity, subband renormalization, intersubband plasmon oscillation, and nonparabolicity of bandstructure. Our results uncover a new perspective for ISBTs and indicate the necessity of proper many-body theoretical treatment in order for modeling and prediction of ISBT line shape.
Critical quasienergy states in driven many-body systems
NASA Astrophysics Data System (ADS)
Bastidas Valencia, Victor Manuel; Engelhardt, Georg; Perez-Fernandez, Pedro; Vogl, Malte; Brandes, Tobias
2015-03-01
A quantum phase transition (QPT) is characterized by non-analyticities of ground-state properties at the critical points. Recently it has been shown that quantum criticality emerges also in excited states of the system, which is referred to as an excited-state quantum phase transition (ESQPT). This kind of quantum criticality is intimately related to a level clustering at critical energies, which results in a logarithmic singularity in the density of states. Most of the previous studies on quantum criticality in excited states have been focused on time independent systems. Here we study spectral singularities that appear in periodically-driven many-body systems and show how the external control allows one to engineer geometrical features of the quasienergy landscape. In particular, we study singularities in the quasienergy spectrum of a fully-connected network consisting of two-level systems with time-dependent interactions. We discuss the characteristic signatures of these singularities in observables like the magnetization, which should be measurable with current technology. The authors gratefully acknowledge financial support by the DFG via grants BRA 1528/7, BRA 1528/8, SFB 910 (V.M.B., T.B.), the Spanish Ministerio de Ciencia e Innovacion (Grants No. FIS2011-28738-C02-01) and Junta de Andalucia (Grants No. FQM160).
On the spectral analysis of many-body systems
Mondher Damak; Vladimir Georgescu
2009-11-26
We describe the essential spectrum and prove the Mourre estimate for quantum particle systems interacting through k-body forces and creation-annihilation processes which do not preserve the number of particles. For this we compute the ``Hamiltonian algebra'' of the system, i.e. the C*-algebra C generated by the Hamiltonians we want to study, and show that, as in the N-body case, it is graded by a semilattice. Hilbert C*-modules graded by semilattices are involved in the construction of C. For example, if we start with an N-body system whose Hamiltonian algebra is B and then we add field type couplings between subsystems, then the many-body Hamiltonian algebra C is the imprimitivity algebra of a graded Hilbert B-module.
Computational nuclear quantum many-body problem: The UNEDF project
Fann, George I
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
A Many Body Eigenvalue Problem for Quantum Computation
NASA Astrophysics Data System (ADS)
Hershfield, Selman
2008-03-01
A one dimensional many body Hamiltonian is presented whose eigenvalues are related to the order of GN. This is the same order of GN used to decode the RSA algorithm. For some values of N the Hamiltonian is a noninteracting fermion problem. For other values of N the Hamiltonian is a quantum impurity problem with fermions interacting with a spin-like object. However, the generic case has fermions or spins interacting with higher order interactions beyond two body interactions. Because this is a mapping between two different classes of problems, one of interest in quantum computing and the other a more traditional condensed matter physics Hamiltonian, we will show (i) how knowledge of the order of GN can be used to solve some novel one dimensional strongly correlated problems and (ii) how numerical techniques, particularly for quantum impurity limit, can be used to find the order of GN.
Irreducible many-body correlations in topologically ordered systems
Yang Liu; Bei Zeng; D. L. Zhou
2014-02-18
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation, the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits irreducible many-body correlation which becomes reducible when the holes are removed. The appearance of these irreducible correlations then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in an external magnetic field, and show that the topological phase transition is signaled by the irreducible many-body correlations.
Ideal quantum glass transitions: Many-body localization without quenched disorder
Schiulaz, M. [International School for Advanced Studies (SISSA), via Bonomea 265, 34136 Trieste (Italy); Müller, M. [The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste (Italy)
2014-08-20
We explore the possibility for translationally invariant quantum many-body systems to undergo a dynamical glass transition, at which ergodicity and translational invariance break down spontaneously, driven entirely by quantum effects. In contrast to analogous classical systems, where the existence of such an ideal glass transition remains a controversial issue, a genuine phase transition is predicted in the quantum regime. This ideal quantum glass transition can be regarded as a many-body localization transition due to self-generated disorder. Despite their lack of thermalization, these disorder-free quantum glasses do not possess an extensive set of local conserved operators, unlike what is conjectured for many-body localized systems with strong quenched disorder.
Determinant method and quantum simulations of many-body effects in a single impurity Anderson model
Gubernatis, J.E.; Olson, T.C.; Scalapino, D.J.; Sugar, R.L.
1986-06-01
We present a short description of a quantum Monte Carlo technique that has proved useful for simulating many-body effects in systems of interacting fermins at finite temperatures. We then report our preliminary results using this technique on a single impurity Anderson model. Examples of such many-body effects as local moment formation, Kondo behavior, and mixed valence phenomena found in the simulations are shown.
MÃ¼ller, Markus
Ideal quantum glass transitions: Many-body localization without quenched disorder M. Schiulaz and M://scitation.aip.org/termsconditions. Downloaded to IP: 87.102.243.104 On: Mon, 18 Aug 2014 14:07:47 #12;Ideal quantum glass transitions: many classical systems, where the existence of such an ideal glass transition remains a controversial issue
Interrogating the void : the difficulty of extracting information from many-body systems
Diab, Kenan S. (Kenan Sebastian)
2011-01-01
In this thesis, I will explore some of the ways the information-theoretic properties of quantum many-body systems can be analyzed. I do this in two different settings. First, I will describe an approach to the "scrambling ...
Many-body methods for nuclear systems at subnuclear densities
Armen Sedrakian; John W. Clark
2007-10-03
This article provides a concise review of selected topics in the many-body physics of low density nuclear systems. The discussion includes the condensation of alpha particles in supernova envelopes, formation of three-body bound states and the BEC-BCS crossover in dilute nuclear matter, and neutrino production in $S$-wave paired superfluid neutron matter.
Phase transitions in fermionic systems with many-body interaction
NASA Technical Reports Server (NTRS)
Bozzolo, G.; Plastino, A.; Ferrante, J.
1989-01-01
A linearized version of the Hartree-Fock method is used as a probe to investigate phase transitions in fermionic systems with many-body interactions. An application to a new exactly solvable model which includes two- and three-body forces is shown.
Measuring entanglement entropy through the interference of quantum many-body twins
Islam, Rajibul; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-01-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is rapidly gaining prominence in diverse fields ranging from condensed matter to quantum gravity. Despite this generality, measuring entanglement remains challenging. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Leveraging our single-site resolved control of ultra-cold bosonic atoms in optical lattices, we prepare and interfere two identical copies of a many-body state. This enables us to directly measure quantum purity, Renyi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly-corre...
Lattice methods for strongly interacting many-body systems
NASA Astrophysics Data System (ADS)
Drut, Joaquín E.; Nicholson, Amy N.
2013-04-01
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic few- and many-body systems, blurring the interfaces between condensed matter, atomic and low-energy nuclear physics. While some of these techniques have been in use in the area of condensed matter physics for a long time, others, such as hybrid Monte Carlo and improved effective actions, have only recently found their way across areas. With this topical review, we aim to provide a modest overview and a status update on a few notable recent developments. For the sake of brevity we focus on zero-temperature, non-relativistic problems. After a short introduction, we lay out some general considerations and proceed to discuss sampling algorithms, observables, and systematic effects. We show selected results on ground- and excited-state properties of fermions in the limit of unitarity. The appendix contains technical details on group theory on the lattice.
Lattice methods for strongly interacting many-body systems
Joaquín E. Drut; Amy N. Nicholson
2013-09-17
Lattice field theory methods, usually associated with non-perturbative studies of quantum chromodynamics, are becoming increasingly common in the calculation of ground-state and thermal properties of strongly interacting non-relativistic few- and many-body systems, blurring the interfaces between condensed matter, atomic and low-energy nuclear physics. While some of these techniques have been in use in the area of condensed matter physics for a long time, others, such as hybrid Monte Carlo and improved effective actions, have only recently found their way across areas. With this topical review, we aim to provide a modest overview and a status update on a few notable recent developments. For the sake of brevity we focus on zero-temperature, non-relativistic problems. After a short introduction, we lay out some general considerations and proceed to discuss sampling algorithms, observables, and systematic effects. We show selected results on ground- and excited-state properties of fermions in the limit of unitarity. The appendix contains details on group theory on the lattice.
Many-body localization in periodically driven systems.
Ponte, Pedro; Papi?, Z; Huveneers, François; Abanin, Dmitry A
2015-04-10
We consider disordered many-body systems with periodic time-dependent Hamiltonians in one spatial dimension. By studying the properties of the Floquet eigenstates, we identify two distinct phases: (i) a many-body localized (MBL) phase, in which almost all eigenstates have area-law entanglement entropy, and the eigenstate thermalization hypothesis (ETH) is violated, and (ii) a delocalized phase, in which eigenstates have volume-law entanglement and obey the ETH. The MBL phase exhibits logarithmic in time growth of entanglement entropy when the system is initially prepared in a product state, which distinguishes it from the delocalized phase. We propose an effective model of the MBL phase in terms of an extensive number of emergent local integrals of motion, which naturally explains the spectral and dynamical properties of this phase. Numerical data, obtained by exact diagonalization and time-evolving block decimation methods, suggest a direct transition between the two phases. PMID:25910094
Fast Convergence of Path Integrals for Many-body Systems
Aleksandar Bogojevic; Ivana Vidanovic; Antun Balaz; Aleksandar Belic
2008-04-17
We generalize a recently developed method for accelerated Monte Carlo calculation of path integrals to the physically relevant case of generic many-body systems. This is done by developing an analytic procedure for constructing a hierarchy of effective actions leading to improvements in convergence of $N$-fold discretized many-body path integral expressions from 1/N to $1/N^p$ for generic $p$. In this paper we present explicit solutions within this hierarchy up to level $p=5$. Using this we calculate the low lying energy levels of a two particle model with quartic interactions for several values of coupling and demonstrate agreement with analytical results governing the increase in efficiency of the new method. The applicability of the developed scheme is further extended to the calculation of energy expectation values through the construction of associated energy estimators exhibiting the same speedup in convergence.
Porter-Thomas distribution in unstable many-body systems
Volya, Alexander
2011-04-15
We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and the collectivity that emerges in nonstationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between the structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.
Porter-Thomas distribution in unstable many-body systems
Alexander Volya
2010-11-24
We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and collectivity that emerges in non-stationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.
Entanglement Theory and the Quantum Simulation of Many-Body Physics
Fernando G. S. L. Brandao
2008-10-21
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum many-body phenomena. In the first part we introduce a new approach to the study of entanglement by considering its manipulation under operations not capable of generating entanglement and show there is a total order for multipartite quantum states in this framework. We also present new results on hypothesis testing of correlated sources and give further evidence on the existence of NPPT bound entanglement. In the second part, we study the potential as well as the limitations of a quantum computer for calculating properties of many-body systems. First we analyse the usefulness of quantum computation to calculate additive approximations to partition functions and spectral densities of local Hamiltonians. We then show that the determination of ground state energies of local Hamiltonians with an inverse polynomial spectral gap is QCMA-hard. In the third and last part, we approach the problem of quantum simulating many-body systems from a more pragmatic point of view. We analyze the realization of paradigmatic condensed matter Hamiltonians in arrays of coupled microcavities, such as the Bose-Hubbard and the anisotropic Heisenberg models, and discuss the feasibility of an experimental realization with state-of-the-art current technology.
Relativistic effects in nuclear many-body systems
Coester, F.
1985-01-01
Different approaches to the formulation of relativistic many-body dynamics yield different perspectives of nature and the magnitude of ''relativistic effects''. The effects of Lorentz invariance appear to be relatively unimportant. Important dynamical features of spinorial many-body formalisms are effects of subnuclear degrees of freedom which are represented in the many-body forces of the covariant nuclear Hamiltonian. 24 refs.
Rotation of Quantum Impurities in the Presence of a Many-Body Environment
NASA Astrophysics Data System (ADS)
Schmidt, Richard; Lemeshko, Mikhail
2015-05-01
We develop a microscopic theory describing a quantum impurity whose rotational degree of freedom is coupled to a many-particle bath. We approach the problem by introducing the concept of an "angulon"—a quantum rotor dressed by a quantum field—and reveal its quasiparticle properties using a combination of variational and diagrammatic techniques. Our theory predicts renormalization of the impurity rotational structure, such as that observed in experiments with molecules in superfluid helium droplets, in terms of a rotational Lamb shift induced by the many-particle environment. Furthermore, we discover a rich many-body-induced fine structure, emerging in rotational spectra due to a redistribution of angular momentum within the quantum many-body system.
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
Johannes Schachenmayer; Alexander Pikovski; Ana Maria Rey
2015-02-25
Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science, and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase-space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.
Critical quasienergy states in driven many-body systems
Victor Manuel Bastidas; Georg Engelhardt; Pedro Perez-Fernandez; Malte Vogl; Tobias Brandes
2015-01-09
We discuss singularities in the spectrum of driven many-body spin systems. In contrast to undriven models, the driving allows us to control the geometry of the quasienergy landscape. As a consequence, one can engineer singularities in the density of quasienergy states by tuning an external control. We show that the density of levels exhibits logarithmic divergences at the saddle points, while jumps are due to local minima of the quasienergy landscape. We discuss the characteristic signatures of these divergences in observables like the magnetization, which should be measurable with current technology.
Lattice simulations for few- and many-body systems
Dean Lee
2008-12-13
We review the recent literature on lattice simulations for few- and many-body systems. We focus on methods and results that combine the framework of effective field theory with computational lattice methods. Lattice effective field theory is discussed for cold atoms as well as low-energy nucleons with and without pions. A number of different lattice formulations and computational algorithms are considered, and an effort is made to show common themes in studies of cold atoms and low-energy nuclear physics as well as common themes in work by different collaborations.
Critical quasienergy states in driven many-body systems
NASA Astrophysics Data System (ADS)
Bastidas, V. M.; Engelhardt, G.; Pérez-Fernández, P.; Vogl, M.; Brandes, T.
2014-12-01
We discuss singularities in the spectrum of driven many-body spin systems. In contrast to undriven models, the driving allows us to control the geometry of the quasienergy landscape. As a consequence, one can engineer singularities in the density of quasienergy states by tuning an external control. We show that the density of levels exhibits logarithmic divergences at the saddle points, while jumps are due to local minima of the quasienergy landscape. We discuss the characteristic signatures of these divergences in observables such as the magnetization, which should be measurable with current technology.
Adiabatic many-body state preparation and information transfer in quantum dot arrays
NASA Astrophysics Data System (ADS)
Farooq, Umer; Bayat, Abolfazl; Mancini, Stefano; Bose, Sougato
2015-04-01
Quantum simulation of many-body systems are one of the most interesting tasks of quantum technology. Among them is the preparation of a many-body system in its ground state when the vanishing energy gap makes the cooling mechanisms ineffective. Adiabatic theorem, as an alternative to cooling, can be exploited for driving the many-body system to its ground state. In this paper, we study two most common disorders in quantum dot arrays, namely exchange coupling fluctuations and hyperfine interaction, in adiabatic preparation of ground state in such systems. We show that the adiabatic ground-state preparation is highly robust against those disorder effects making it a good analog simulator. Moreover, we also study the adiabatic quantum information transfer, using singlet-triplet states, across a spin chain. In contrast to ground-state preparation the transfer mechanism is highly affected by disorder and in particular, the hyperfine interaction is very destructive for the performance. This suggests that for communication tasks across such arrays adiabatic evolution is not as effective and quantum quenches could be preferable.
Many-body transverse interactions in the quantum annealing of the p-spin ferromagnet
Beatriz Seoane; Hidetoshi Nishimori
2012-10-10
We study the performance of quantum annealing for the simple $p$-body infinite-range ferromagnetic Ising model. In particular, we generalize the transverse antiferromagnetic interactions proposed by Seki and Nishimori as a quantum driver to many-body transverse interactions to understand if the two-body interactions are essential to allow the system to avoid troublesome first-order quantum phase transitions. We conclude that the general many-body interactions are effective to let the system evolve only through second-order transitions as long as a few minor conditions are satisfied. It is also discussed whether the overlap of the ground-state wave function of the new driver term with the target ground state is an essential factor for the success.
Adiabatic many-body state preparation and information transfer in quantum dot arrays
Umer Farooq; Abolfazl Bayat; Stefano Mancini; Sougato Bose
2015-04-27
Quantum simulation of many-body systems are one of the most interesting tasks of quantum technology. Among them is the preparation of a many-body system in its ground state when the vanishing energy gap makes the cooling mechanisms ineffective. Adiabatic theorem, as an alternative to cooling, can be exploited for driving the many-body system to its ground state. In this paper, we study two most common disorders in quantum dot arrays, namely exchange coupling fluctuations and hyperfine interaction, in adiabatically preparation of ground state in such systems. We show that the adiabatic ground state preparation is highly robust against those disorder effects making it good analog simulator. Moreover, we also study the adiabatic classical information transfer, using singlet-triplet states, across a spin chain. In contrast to ground state preparation the transfer mechanism is highly affected by disorder and in particular, the hyperfine interaction is very destructive for the performance. This suggests that for communication tasks across such arrays adiabatic evolution is not as effective and quantum quenches could be preferable.
Andreas Gabriel; Beatrix C. Hiesmayr
2013-03-01
We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum computation, our methods can be used to select or design appropriate condensed matter systems.
A many-body approach to quantum transport dynamics: Initial correlations and memory effects
NASA Astrophysics Data System (ADS)
Myöhänen, P.; Stan, A.; Stefanucci, G.; van Leeuwen, R.
2008-12-01
We study time-dependent quantum transport through a correlated double quantum dot (DQD) model system by means of time propagation of the nonequilibrium many-body Green's function. The theory is an extension of the Kadanoff-Baym approach for finite inhomogeneous systems (Phys. Rev. Lett., 98 (2007) 153004) to open inhomogeneous systems and generalizes the Meir-Wingreen formula to include initial correlations and memory effects. Important features of the theory are 1) the possibility to study the ultrafast dynamics of transients and other time-dependent regimes and 2) the inclusion of exchange and correlation effects in a conserving approximation scheme. We calculate time-dependent local currents and densities for different many-body approximations and highlight the role of initial correlations and memory effects on the transient dynamics. Furthermore we show that coherent charge oscillations on the DQD are strongly affected by the confined Coulomb interaction and can be directly related to the local equilibrium spectral density.
Phase-space characterization of complexity in quantum many-body dynamics.
Balachandran, Vinitha; Benenti, Giuliano; Casati, Giulio; Gong, Jiangbin
2010-10-01
We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well-known measure of complexity in classical systems and which is valid for both pure and mixed states in single-particle and many-body systems, takes into account the combined role of chaos and entanglement in the realm of quantum mechanics. The effectiveness of the measure is illustrated in the example of the Ising chain in a homogeneous tilted magnetic field. We provide numerical evidence that the multipartite entanglement generation leads to a linear increase in entropy until saturation in both integrable and chaotic regimes, so that in both cases the number of harmonics of the Wigner function grows exponentially with time. The entropy growth rate can be used to detect quantum phase transitions. The proposed entropy measure can also distinguish between integrable and chaotic many-body dynamics by means of the size of long-term fluctuations which become smaller when quantum chaos sets in. PMID:21230374
Many body physics and the capacity of quantum channels with memory
M. B. Plenio; S. Virmani
2008-03-20
In most studies of the capacity of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error, and has led to suggestions that there can be interesting non-analytic behaviour in the capacity of such channels. In a previous paper we pursued this issue by connecting the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables the use of techniques from many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error with analogous behaviour to associated many-body systems. However, in order for this approach to work rigorously, there are a number of technical properties that need to be established for the lattice systems being considered. In this article we discuss these properties in detail, and establish them for some classes of many-body system.
Exploring dynamics of unstable many-body systems
Volya, Alexander [Department of Physics, Florida State University, Tallahassee, FL 32306-4350 (United States); Zelevinsky, Vladimir [National Superconducting Cyclotron Laboratory and Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-1321 (United States)
2014-10-15
In this work we acquaint reader with the Continuum Shell Model (CSM), which is a proper theoretical tool for the description of physics of unstable systems. We describe the effective non-Hermitian Hamiltonian of the CSM and concentrate on specific aspects of dynamics using realistic examples. The continuum effects are discussed in the case of weakly bound heavy oxygen isotopes, where inclusion of continuum coupling is necessary to improve the traditional nuclear shell model techniques. Physics of overlapping resonances is illustrated using recent experimental information on {sup 8}B nucleus. In the limit of strong continuum coupling the many-body states restructure relative to continuum leading to a few very broad super-radiant states, while at the same time other states become narrow and nearly decoupled from decay. The recent observations of very broad alpha clustering states in {sup 18}O is one of the most transparent manifestations of super-radiance.
A two-band Bose-Hubbard model for many-body resonant tunneling in the Wannier-Stark system
Carlos A. Parra-Murillo; Javier Madroñero; Sandro Wimberger
2013-06-11
We study an experimentally realizable paradigm of complex many-body quantum systems, a two-band Wannier-Stark model, for which diffusion in Hilbert space as well as many-body Landau-Zener processes can be engineered. A cross-over between regular to quantum chaotic spectra is found within the many-body avoided crossings at resonant tunneling conditions. The spectral properties are shown to determine the evolution of states across a cascade of Landau-Zener events. We apply the obtained spectral information to study the non-equilibrium dynamics of our many-body system in different parameter regimes.
Quantum drude oscillators for accurate many-body intermolecular forces
Jones, Andrew
2010-01-01
One of the important early applications of Quantum Mechanics was to explain the Van-der-Waal’s 1/R6 potential that is observed experimentally between two neutral species, such as noble gas atoms, in terms of correlated ...
Bosonic many-body theory of quantum spin ice
NASA Astrophysics Data System (ADS)
Hao, Zhihao; Day, Alexandre G. R.; Gingras, Michel J. P.
2014-12-01
We carry out an analytical study of quantum spin ice, a U (1 ) quantum spin liquid close to the classical spin-ice solution for an effective spin-1/2 model with anisotropic exchange couplings Jz z, J±, and Jz ± on the pyrochlore lattice. Starting from the quantum rotor model introduced by Savary and Balents [Phys. Rev. Lett. 108, 037202 (2012), 10.1103/PhysRevLett.108.037202], we retain the dynamics of both the spinons and gauge field sectors in our treatment. The spinons are described by a bosonic representation of quantum XY rotors, while the dynamics of the gauge field is captured by a phenomenological Hamiltonian. By calculating the one-loop spinon self-energy, which is proportional to Jz± 2, we determine the stability region of the U (1 ) quantum spin-liquid phase in the J±/Jz z versus Jz ±/Jz z zero-temperature phase diagram. From these results, we estimate the location of the boundaries between the spin-liquid phase and classical long-range ordered phases.
Many-body calculation for charge transport through triangular quantum dot molecules
NASA Astrophysics Data System (ADS)
Chen, Chih-Chieh; Chang, Yia-Chung; Kuo, David M. T.
2015-03-01
We study the many-body effect of electron tunneling through the coupled quantum dots systems in the Coulomb blockade regime. Using the equation of motion method for the non-equilibrium Green's function, we calculate the charge current and conductance of junctions consisting of metallic electrodes and a few quantum dots. Many-particle correlation functions are explicitly solved numerically. Quantum phenomena like quantum interference, Coulomb blockade and spin blockade for the triangular quantum dot molecules are discussed. Our work suggests a new method for the modeling of the mesoscopic transport. This work was supported in part by the Ministry of Science and Technology, Taiwan under Contract Nos. NSC 101-2112-M-001-024-MY3 and NSC 103-2112-M-008-009-MY3.
Many-body localization in a quantum simulator with programmable random disorder
Smith, Jacob; Richerme, Philip; Neyenhuis, Brian; Hess, Paul W; Hauke, Philipp; Heyl, Markus; Huse, David A; Monroe, Christopher
2015-01-01
When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the e...
NASA Astrophysics Data System (ADS)
Hermanns, S.; Balzer, K.; Bonitz, M.
2012-11-01
In the non-equilibrium Green function calculations, the use of the generalized Kadanoff-Baym ansatz (GKBA) allows for a simple approximate reconstruction of the two-time Green function from its time-diagonal value. With this, a drastic reduction of the computational needs is achieved in time-dependent calculations, making longer time propagation possible and more complex systems accessible. This paper gives credit to the GKBA that was introduced 25 years ago. After a detailed derivation of the GKBA, we recall its application to homogeneous systems and show how to extend it to strongly correlated, inhomogeneous systems. As a proof of concept, we present the results for a two-electron quantum well, where the correct treatment of the correlated electron dynamics is crucial for a correct description of the equilibrium and dynamic properties.
Conservative chaotic map as a model of quantum many-body environment
Davide Rossini; Giuliano Benenti; Giulio Casati
2006-06-08
We study the dynamics of the entanglement between two qubits coupled to a common chaotic environment, described by the quantum kicked rotator model. We show that the kicked rotator, which is a single-particle deterministic dynamical system, can reproduce the effects of a pure dephasing many-body bath. Indeed, in the semiclassical limit the interaction with the kicked rotator can be described as a random phase-kick, so that decoherence is induced in the two-qubit system. We also show that our model can efficiently simulate non-Markovian environments.
Amplification and suppression of system-bath correlation effects in an open many-body system
Adam Zaman Chaudhry; Jiangbin Gong
2012-11-21
Understanding the rich dynamics of open quantum systems is of fundamental interest to quantum control and quantum information processing. By considering an open system of many identical two-level atoms interacting with a common bath, we show that effects of system-bath correlations are amplified in a many-body system via the generation of a short time scale inversely proportional to the number of atoms. Effects of system-bath correlations are therefore considerable even when each individual atom interacts with the bath weakly. We further show that correlation-induced dynamical effects may still be suppressed via the dynamical decoupling approach, but they present a challenge for quantum state protection as the number of atom increases.
Quantum Simulation with Circuit-QED Lattices: from Elementary Building Blocks to Many-Body Theory
NASA Astrophysics Data System (ADS)
Zhu, Guanyu
Recent experimental and theoretical progress in superconducting circuits and circuit QED (quantum electrodynamics) has helped to develop high-precision techniques to control, manipulate, and detect individual mesoscopic quantum systems. A promising direction is hence to scale up from individual building blocks to form larger-scale quantum many-body systems. Although realizing a scalable fault-tolerant quantum computer still faces major barriers of decoherence and quantum error correction, it is feasible to realize scalable quantum simulators with state-of-the-art technology. From the technological point of view, this could serve as an intermediate stage towards the final goal of a large-scale quantum computer, and could help accumulating experience with the control of quantum systems with a large number of degrees of freedom. From the physical point of view, this opens up a new regime where condensed matter systems can be simulated and studied, here in the context of strongly correlated photons and two-level systems. In this thesis, we mainly focus on two aspects of circuit-QED based quantum simulation. First, we discuss the elementary building blocks of the quantum simulator, in particular a fluxonium circuit coupled to a superconducting resonator. We show the interesting properties of the fluxonium circuit as a qubit, including the unusual structure of its charge matrix elements. We also employ perturbation theory to derive the effective Hamiltonian of the coupled system in the dispersive regime, where qubit and the photon frequencies are detuned. The observables predicted with our theory, including dispersive shifts and Kerr nonlinearity, are compared with data from experiments, such as homodyne transmission and two-tone spectroscopy. These studies also relate to the problem of detection in a circuit-QED quantum simulator. Second, we study many-body physics of circuit-QED lattices, serving as quantum simulators. In particular, we focus on two different directions which complement each other. One is concerned with quantum phases, such as photon pairing states, arising from the specific nature of light-matter interaction not usually encountered in conventional condensed matter materials. The second deals with interacting photons in a very specific lattice, the Kagome lattice. In that case, interesting liquid-crystal-like quantum phases, such as a nematic superfluid and a Wigner crystal, arise from the geometric frustration of the lattice.
Experimental quantum simulations of many-body physics with trapped ions.
Schneider, Ch; Porras, Diego; Schaetz, Tobias
2012-02-01
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems. PMID:22790343
Particle number conservation in quantum many-body simulations with matrix product operators
NASA Astrophysics Data System (ADS)
Muth, Dominik
2011-11-01
Incorporating conservation laws explicitly into matrix product states (MPSs) has proven to make numerical simulations of quantum many-body systems much less resource consuming. We will discuss here to what extent this concept can be used in simulation where the dynamically evolving entities are matrix product operators (MPOs). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that often the entanglement imposed by the global constraint of fixed particle number is the limiting factor.
Particle number conservation in quantum many-body simulations with matrix product operators
Muth, Dominik
2011-01-01
Incorporating conservation laws explicitly into Matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that often the entanglement imposed by the global constraint of fixed particle number is the limiting factor in the canonical ensemble.
Static self-gravitating many-body systems in Einstein gravity
Lars Andersson; Berndt G. Schmidt
2009-05-08
We consider the problem of constructing static, elastic, many-body systems in Einstein gravity. The solutions constructed are deformations of static many-body configurations in Newtonian gravity. No symmetry assumptions are made.
The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations
Sellier, J.M. Dimov, I.
2014-09-15
The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practically unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.
Many-Body Effects and Lineshape of Intersubband Transitions in Semiconductor Quantum Wells
NASA Technical Reports Server (NTRS)
Ning, Cun-Zheng
2003-01-01
Intersubband Transition (ISBT) infrared (IR) absorption and PL in InAs/AlSb were studied for narrow Quantum Wells (QWs). A large redshift was observed (7-10 meV) as temperature increased. A comprehensive many-body theory was developed for ISBTs including contributions of c-c and c-phonon scatterings. Many-body effects were studied systematically for ISBTs. Redshift and linewidth dependence on temperature, as well as spectral features were well explained by theory.
A remark on the mean-field dynamics of many-body bosonic systems with random interactions
Walid K. Abou Salem
2007-11-16
The mean-field limit for the dynamics of bosons with random interactions is rigorously studied. It is shown that, for interactions that are almost-surely bounded, the many-body quantum evolution can be replaced in the mean-field limit by a single particle nonlinear evolution that is described by the Hartree equation. This is an Egorov-type theorem for many-body quantum systems with random interactions.
221B Lecture Notes Many-Body Problems I (Quantum Statistics)
Murayama, Hitoshi
221B Lecture Notes Many-Body Problems I (Quantum Statistics) 1 Quantum Statistics of Identical Particles If two particles are identical, their exchange must not change physical quan- tities. Therefore is for bosons (particles that obey BoseEinstein statistics) and -1 for fermions (those that obey Fermi
Rigol, Marcos [Physics Department, University of California, Davis, California 95616 (United States); Dunjko, Vanja; Olshanii, Maxim [Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089 (United States); Institute for Theoretical Atomic and Molecular Physics, Cambridge, Massachusetts 02138 (United States); Yurovsky, Vladimir [School of Chemistry, Tel Aviv University, Tel Aviv 69978 (Israel)
2007-02-02
In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)].
Extraction of Pure Entangled States from Many Body Systems by Distant Local Projections
J. Molina-Vilaplana; H. Wichterich; V. E. Korepin; S. Bose
2009-03-26
We study the feasibility of extracting a pure entangled state of non-complementary, and potentially well separated, regions of a quantum many-body system. It is shown that this can indeed be accomplished in non-equilibrium scenarios as well as the ground state of the considered spin chain models when one locally measures observables such as magnetization in separated blocks of spins. A general procedure is presented, which can search for the optimal way to extract a pure entangled state through local projections. Our results indicate a connection of the projective extraction of entanglement to good quantum numbers of the underlying Hamiltonian.
Rotation of quantum impurities in the presence of a many-body environment
NASA Astrophysics Data System (ADS)
Lemeshko, Mikhail; Schmidt, Richard
2015-05-01
Pioneered by the seminal works of Wigner and Racah, the quantum theory of angular momentum evolved into a powerful machinery, commonly used to classify the states of isolated quantum systems and perturbations to their structure due to electromagnetic or crystalline fields. In ``realistic'' experiments, however, quantum systems are almost inevitably coupled to a many-particle environment and a field of elementary excitations associated with it, which is capable of fundamentally altering the physics of the system. We present the first systematic treatment of quantum rotation coupled to a many-particle environment. By using a series of canonical transformations on a generic microscopic Hamiltonian, we single out the conserved quantities of the problem. Using a variational ansatz accounting for an infinite number of many-body excitations, we characterize the spectrum of angular momentum eigenstates and identify the regions of instability, accompanied by emission of angular Cerenkov radiation. The developed technique can be applied to a wide range of systems described by the angular momentum algebra, from Rydberg atoms immersed into BEC's, to cold molecules solvated in helium droplets, to ultracold molecular ions.
Few-Body and Many-Body Quantum Optics in Rydberg Media
NASA Astrophysics Data System (ADS)
Gorshkov, Alexey
2014-03-01
We theoretically describe the propagation of quantized light under the conditions of electromagnetically induced transparency (EIT) in systems involving Rydberg states. In these systems, EIT enables the mapping of strong interactions between Rydberg atoms onto strong interactions between photons. We show how to make photons massive and how to introduce attractive, repulsive, and dissipative interactions between them. We also find and study the propagation of solitonic bound states of photons in such a medium. Finally, we determine the peculiar spatiotemporal structure of the output of two complementary Rydberg-EIT-based light-processing modules: the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. Our approach paves the way for the generation of a variety of nonclassical states of light, the implementation of photon-photon quantum gates, and the study of many-body phenomena with strongly correlated photons.
Exact numerical methods for a many-body Wannier-Stark system
NASA Astrophysics Data System (ADS)
Parra-Murillo, Carlos A.; Madroñero, Javier; Wimberger, Sandro
2015-01-01
We present exact methods for the numerical integration of the Wannier-Stark system in a many-body scenario including two Bloch bands. Our ab initio approaches allow for the treatment of a few-body problem with bosonic statistics and strong interparticle interaction. The numerical implementation is based on the Lanczos algorithm for the diagonalization of large, but sparse symmetric Floquet matrices. We analyze the scheme efficiency in terms of the computational time, which is shown to scale polynomially with the size of the system. The numerically computed eigensystem is applied to the analysis of the Floquet Hamiltonian describing our problem. We show that this allows, for instance, for the efficient detection and characterization of avoided crossings and their statistical analysis. We finally compare the efficiency of our Lanczos diagonalization for computing the temporal evolution of our many-body system with an explicit fourth order Runge-Kutta integration. Both implementations heavily exploit efficient matrix-vector multiplication schemes. Our results should permit an extrapolation of the applicability of exact methods to increasing sizes of generic many-body quantum problems with bosonic statistics.
The definition of the velocity field in many body systems
B. B. Varga; S. G. Eckstein
1969-01-01
Contrary to the usual assumption of quantum hydrodynamics a velocity field cannot be uniquely defined at each point of space because the inverse density operator does not exist. A physically meaningful velocity field is constructed without using the inverse density field.
Geometric phases induced in auxiliary qubits by many-body systems near its critical points
X. X. Yi; W. Wang
2007-03-07
The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the qubit, respectively. As an example, we consider the XY spin-chain dephasingly couple to a qubit, the geometric phase induced in the qubit is presented and discussed. The results show that the geometric phase might be used to signal the critical points of the many-body system, and it tends to zero with the parameters of the many-body system going away from the critical points.
Nikitin, Anatoly
REVISTA MEXICANA DE F´ISICA ?? SUPLEMENTO *?*, ?????? MES? A ~NO? The many body problem in relativistic quantum mechanics M. Moshinsky* and A. Nikitin Instituto de F´isica, Universidad Nacional Aut´onoma de M´exico, Apartado Postal 20-364, 01000 M´exico D.F., M´exico e-mail: moshi@fisica.unam.mx Recibido
Dissipative Many-Body Quantum Optics in Rydberg Media Alexey V. Gorshkov,1,2
, 32.80.Ee, 34.20.Cf, 42.50.Gy Dissipation has recently been recognized as a powerful tool for quantum the many-body density matrix of the light field; i.e., it faithfully describes the process of populating
Observation of a many-body edge singularity in quantum well luminescence spectra
NASA Astrophysics Data System (ADS)
Skolnick, M. S.; Rorison, J. M.; Nash, K. J.; Mowbray, D. J.; Tapster, P. R.; Bass, S. J.; Pitt, A. D.
1987-05-01
The observation of a many-body, Fermi energy edge singularity in the low-temperature photoluminescence spectra of InGaAs-InP quantum wells is reported. Strong enhancement of the photoluminescence intensity towards the electron Fermi energy (EFe) is observed, due to multiple electron-hole scattering processes to states above EFe. Recombination of electrons in states up to EFe is allowed by hole localization. The many-body processes are analogous to the core-hole phenomena in the soft x-ray emission spectra of metals.
Mean field approximation of many-body quantum dynamics for Bosons in a discrete numerical model
Boris Pawilowski
2015-08-03
The mean field approximation is numerically validated in the bosonic case by considering the time evolution of quantum states and their associated reduced density matrices by many-body Schr\\"odinger dynamics. The model phase-space is finite-dimensional. The results are illustrated with numerical simulations of the evolution of quantum states according to the time, the number of the particles, and the dimension of the phase-space.
Many-body systems in Einstein-Maxwell-Dilaton theory
Kiyoshi Shiraishi
1995-07-14
We study the interaction of maximally-charged dilatonic black holes at low velocity. We compute the metric on moduli space for three extreme black holes under a simple constraint. The Hamiltonian of the multi-black hole system of $O(v^2)$ is also calculated for the $a=1$ and $a=1/\\sqrt{3}$ cases, where $a$ is the dilaton coupling constant. The behavior of the system is discussed qualitatively.
Many-Body Force and Mobility Measurements in Colloidal Systems
Jason W. Merrill; Sunil K. Sainis; Jerzy Blawzdziewicz; Eric R. Dufresne
2009-12-22
We demonstrate a technique for simultaneously measuring each component of the force vectors and mobility tensor of a small collection of colloidal particles based on observing a set of particle trajectories. For a few-body system of micron-sized polymer beads in oil separated by several particle radii, we find that the mobility tensor is well-described by a pairwise Stokeslet model. This stands in contrast to the electrostatic interactions, which were found to deviate significantly from a pairwise model. The measurement technique presented here should be simple to extend to systems of heterogeneous, non-spherical particles arranged in arbitrary 3D geometries.
Classical Loschmidt echo in chaotic many-body systems
Gregor Veble; Tomaz Prosen
2005-03-21
General theoretic approach to classical Loschmidt echoes in chaotic systems with many degrees of freedom is developed. For perturbations which affect essentially all degrees of freedom we find a doubly exponential decay with the rate determined by the largest Lyapunov exponent. The scaling of the decay rate on the perturbation strength depends on whether the initial phase-space density is continuous or not.
Order-disorder transitions in a sheared many body system
Pfeifer, Jens C; Ehlers, Georg; Eckhardt, Bruno
2015-01-01
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped 2-d system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essent...
Many-body effects in wide parabolic AlGaAs quantum wells
NASA Astrophysics Data System (ADS)
Tabata, A.; Martins, M. R.; Oliveira, J. B. B.; Lamas, T. E.; Duarte, C. A.; da Silva, E. C. F.; Gusev, G. M.
2007-11-01
Photoluminescence measurements at different temperatures have been performed to investigate the optical response of a two-dimensional electron gas in n-type wide parabolic quantum wells. A series of samples with different well widths in the range of 1000-3000Å was analyzed. Many-body effects, usually observed in the recombination process of a two-dimensional electron gas, appear as a strong enhancement in the photoluminescence spectra at the Fermi level at low temperature only in the thinnest parabolic quantum wells. The suppression of the many-body effect in the thicker quantum wells was attributed to the decrease of the overlap between the wavefunctions of the photocreated holes and the two-dimensional electrons belonging to the highest occupied electron subband.
Aging dynamics in interacting many-body systems
Sanders, Lloyd P; Lizana, Ludvig; Fogelmark, Karl; Metzler, Ralf; Ambjörnsson, Tobias
2013-01-01
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly disordered, one-dimensional environment. Each particle in this single file is trapped for a random waiting time $\\tau$ with power law distribution $\\psi(\\tau)\\simeq\\tau^{-1- \\alpha}$, such that the $\\tau$ values are independent, local quantities for all particles. From scaling arguments and simulations, we find that for the scale-free waiting time case $02$ we recover Harris law $\\simeq t^{1/2}$.
Order-disorder transitions in a sheared many body system
Jens C. Pfeifer; Tobias Bischoff; Georg Ehlers; Bruno Eckhardt
2015-07-17
Motivated by experiments on sheared suspensions that show a transition between ordered and disordered phases, we here study the long-time behavior of a sheared and overdamped 2-d system of particles interacting by repulsive forces. As a function of interaction strength and shear rate we find transitions between phases with vanishing and large single-particle diffusion. In the phases with vanishing single-particle diffusion, the system evolves towards regular lattices, usually on very slow time scales. Different lattices can be approached, depending on interaction strength and forcing amplitude. The disordered state appears in parameter regions where the regular lattices are unstable. Correlation functions between the particles reveal the formation of shear bands. In contrast to single particle densities, the spatially resolved two-particle correlation functions vary with time and allow to determine the phase within a period. As in the case of the suspensions, motion in the state with low diffusivity is essentially reversible, whereas in the state with strong diffusion it is not.
Computational approaches to many-body dynamics of unstable nuclear systems
Alexander Volya
2014-12-19
The goal of this presentation is to highlight various computational techniques used to study dynamics of quantum many-body systems. We examine the projection and variable phase methods being applied to multi-channel problems of scattering and tunneling; here the virtual, energy-forbidden channels and their treatment are of particular importance. The direct time-dependent solutions using Trotter-Suzuki propagator expansion provide yet another approach to exploring the complex dynamics of unstable systems. While presenting computational tools, we briefly revisit the general theory of the quantum decay of unstable states. The list of questions here includes those of the internal dynamics in decaying systems, formation and evolution of the radiating state, and low-energy background that dominates at remote times. Mathematical formulations and numerical approaches to time-dependent problems are discussed using the quasi-stationary methods involving effective Non-Hermitian Hamiltonian formulation.
Supporting Information for: Electrostatically Embedded Many-Body Expansion for Large Systems, with
Truhlar, Donald G
S1 Supporting Information for: Electrostatically Embedded Many-Body Expansion for Large Systems S3 #12;Results for Truncation after V1 In the traditional many-body expansion, since results with only one-body terms are expected to be poor, equation 1 is rarely truncated after the first term. One
IASSNS-HEP-91/23 Many-body Systems with Non-Abelian Statistics *
Wen, Xiao-Gang
IASSNS-HEP-91/23 May 1991 Many-body Systems with Non-Abelian Statistics * B. Blok and X. G. Wen with the non-abelian statistics. The explicit forms of the many-body ground-state wave functions are calculated. We discuss the calculation of the quasiparticle statistics from the low energy effective theory
Algorithm for simulation of quantum many-body dynamics using dynamical coarse-graining
Khasin, M.; Kosloff, R.
2010-04-15
An algorithm for simulation of quantum many-body dynamics having su(2) spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables--the elements of the spectrum-generating algebra--is simulated by a surrogate open-system dynamics, which can be interpreted as weak measurement of the target observables, performed on the evolving system. The open-system state can be represented by a mixture of pure states, localized in the phase space. The localization reduces the scaling of the computational resources with the Hilbert-space dimension n by factor n{sup 3/2}(ln n){sup -1} compared to conventional sparse-matrix methods. The guidelines for the choice of parameters for the simulation are presented and the scaling of the computational resources with the Hilbert-space dimension of the system is estimated. The algorithm is applied to the simulation of the dynamics of systems of 2x10{sup 4} and 2x10{sup 6} cold atoms in a double-well trap, described by the two-site Bose-Hubbard model.
INTRODUCTION: Many-Body Theory of Atomic Systems: Proceedings of the Nobel Symposium 46
NASA Astrophysics Data System (ADS)
Lindgren, Ingvar; Lundqvist, Stig
1980-01-01
A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating meeting. The Nobel Symposia are very small meetings by invitation only and the number of key participants is usually in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. They have been made possible through a major grant from the Tri-Centennial Fund of the Bank of Sweden. Our first ideas to arrange a Nobel Symposium on many-body theory of atomic systems came up more than two years ago. It was quite obvious to us that a major break-through was happening in this field. Very accurate schemes have been available for some time for studying the static properties of small closed-shell atomic systems. By "atomic" systems we understand here atoms as well as free molecules, which can be treated by the same formalism, although the technical approaches might be quite different. The conceptual and computational developments in recent years, however, have made it possible to apply the many-body formalism also to heavier systems. Although no rigorous relativistic many-body theory yet exists, there seems to be a general agreement about the way relativistic calculations should be performed on normal atoms and molecules. Schemes based on relativistic perturbation theory as well as on relativistic multi- configurational Hartree-Fock are now in operation and a rapid development is expected in this area. Another field of atomic theory, where significant progress has been made recently, is in the application of many-body formalism to open-shell systems. General schemes, applicable to systems with one or several open shells, are now available, which will make it possible to apply many-body formalism to a much larger group of atomic systems and, in particular, to systems of more physical interest, A number of atomic properties - not only the correlation energy - can then be compared with the corresponding experimental results, which will eventually lead to a better understanding of the behaviour of many-electron systems and possibly also of many-fermion systems in general. In addition to the static properties of atomic systems there is nowadays a great interest in the dynamics of the excitation process, which is of fundamental importance for our understanding of photoelectron and photoabsorption spectra. The experimental data being produced in this field are enormous and many intricate physical problems appear, which can only be understood by considering the atom as a fully interacting many-body system. All the new developments mentioned here have opened entirely new areas in atomic many-body theory, and we are evidently just at the verge of a very interesting period of rapid progress. It is quite evident that we could have limited the Symposium to atomic problems of the type described here. However, related problems appear in atoms bound in solids and in atoms/molecules bound to solid surfaces. Therefore, we proposed to include also some aspects of these fields in our program, which brought together scientists with different backgrounds, such as atomic and molecular physicists, theoretical chemists, solid state and surface physicists as well as nuclear physicists and quantum- liquid experts. The Symposium then got a distinctive inter-disciplinary character at the same time as it was concentrated on the specific atomic many-body problem. The response to our invitations to the Nobel Symposium was overwhelming. Many other participants were suggested and we extended the number of participants as far as we could. With the wide scope of the Symposium program and small format with regard to number, only a few representatives of each major area could be invited. The symposium gave an excellent picture how the various areas are developing. The various methods to treat the many-body problem were thoroughly discussed and many new results were reported. The relativistic many-body problem offers many challenging problems as does the open-shell many-body fo
Quantum simulation of many-body physics with neutral atoms, molecules, and ions
NASA Astrophysics Data System (ADS)
Foss-Feig, Michael
2013-05-01
The achievement of quantum degeneracy in alkali vapors has enabled the simulation of iconic condensed-matter models. However, ultracold alkali atoms are not yet cold enough to simulate the most interesting and poorly understood low-temperature properties of those models. In this talk, I will emphasize how the rich internal structure of alkaline earth atoms, ions, and molecules can be leveraged to simulate complex many-body physics in presently accessible experimental settings. I will begin by examining how alkaline earth atoms can be used to simulate the physics of so-called heavy fermion materials, and will show how the exotic groundstate properties of those materials manifests in non-equilibrium dynamics at relatively warm temperatures. Not surprisingly, the rich structure of alkaline earth atoms and molecules comes with a price, in many cases increasing the susceptibility of these systems to decoherence. A particularly troubling feature common to alkaline earth atoms and many molecules is the possibility of two-body loss. However, I will show that such loss can be harnessed to drive optically excited alkaline earth atoms and reactive molecules into highly-entangled non-equilibrium steady states, which could be used in the near future to improve the accuracy of high precision atomic clocks operated with alkaline earth atoms. The fate of interacting quantum systems in the presence of decoherence is of interest much more broadly, and I will conclude by describing how trapped ion systems provide a natural platform for addressing this issue. In particular, I will describe an exact solution of the dissipative Ising models that govern trapped ion systems, which affords both a qualitative and quantitative understanding of the effects of decoherence on these large-scale quantum simulators.
Wang Qi; Sergey Yu. Kun; Tian Wendong; Li Songlin; Jiang Zhonghe; Dong Yuchuan; Li Zhichang; Lu Xiuqin; Zhao Kui; Fu Changbo; Liu Jiancheng; Jiang Hua; Hu Guiqing; W. Greiner
2003-05-08
We have tested recent suggestion of anomalous sensitivity in highly excited quantum many-body systems. Two independent measurements of cross sections for the 19F+93Nb strongly dissipative heavy-ion collisions have been performed at incident energies from 102 to 108 MeV in steps of 250 keV.In the two measurements we used different, independently prepared, 93Nb target foils with nominally the same thickness.The data indicate statistically significant non-reproducibility of the energy oscillating yields in the two measurements. The observed non-reproducibility is consistent with recent theoretical arguments on spontaneous correlation, slow phase randomization and chaos in highly excited complex quantum systems.
Derivation of the two-dimensional nonlinear Schrodinger equation from many body quantum dynamics
Kirkpatrick, Kay
We derive rigorously, for both ${\\Bbb R}^2$ and $[{-}L,L]^{\\times 2}$, the cubic nonlinear Schr\\"odinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair ...
An Explicit Bound for Dynamical Localisation in an Interacting Many-Body System
P. -L. Giscard; Z. Choo; M. T. Mitchison; J. J. Mendoza-Arenas; D. Jaksch
2014-02-06
We characterise and study dynamical localisation of a finite interacting quantum many-body system. We present explicit bounds on the disorder strength required for the onset of localisation of the dynamics of arbitrary ensemble of sites of the XYZ spin-1/2 model. We obtain these results using a novel form of the fractional moment criterion, which we establish, together with a generalisation of the self-avoiding walk representation of the system Green's functions, called path-sums. These techniques are not specific to the XYZ model and hold in a much more general setting. We further present bounds for two observable quantities in the localised regime: the magnetisation of any sublattice of the system as well as the linear magnetic response function of the system. We confirm our results through numerical simulations.
Radiative heat transfer in anisotropic many-body systems: Tuning and enhancement
Nikbakht, Moladad
2014-09-07
A general formalism for calculating the radiative heat transfer in many body systems with anisotropic component is presented. Our scheme extends the theory of radiative heat transfer in isotropic many body systems to anisotropic cases. In addition, the radiative heating of the particles by the thermal bath is taken into account in our formula. It is shown that the radiative heat exchange (HE) between anisotropic particles and their radiative cooling/heating (RCH) could be enhanced several order of magnitude than that of isotropic particles. Furthermore, we demonstrate that both the HE and RCH can be tuned dramatically by particles relative orientation in many body systems.
Braunecker, Bernd
Many-Body Dynamics of Exciton Creation in a Quantum Dot by Optical Absorption: A Quantum Quench to a Fermionic reservoir, induced by the sudden creation of an exciton via optical absorption. The subsequent in quantum dots [5Â7] offer an alternative arena for probing Kondo quenches: the creation of a bound electron
On the rate of convergence for the mean field approximation of many-body quantum dynamics
Zied Ammari; Marco Falconi; Boris Pawilowski
2014-11-23
We consider the time evolution of quantum states by many-body Schr\\"odinger dynamics and study the rate of convergence of their reduced density matrices in the mean field limit. If the prepared state at initial time is of coherent or factorized type and the number of particles $n$ is large enough then it is known that $1/n$ is the correct rate of convergence at any time. We show in the simple case of bounded pair potentials that the previous rate of convergence holds in more general situations with possibly correlated prepared states. In particular, it turns out that the coherent structure at initial time is unessential and the important fact is rather the speed of convergence of all reduced density matrices of the prepared states. We illustrate our result with several numerical simulations and examples of multi-partite entangled quantum states borrowed from quantum information.
Derivation of nonlinear Gibbs measures from many-body quantum mechanics
Mathieu Lewin; Phan Thành Nam; Nicolas Rougerie
2015-05-21
We prove that nonlinear Gibbs measures can be obtained from the corresponding many-body, grand-canonical, quantum Gibbs states, in a mean-field limit where the temperature T diverges and the interaction behaves as 1/T. We proceed by characterizing the interacting Gibbs state as minimizing a functional counting the free-energy relatively to the non-interacting case. We then perform an infinite-dimensional analogue of phase-space semiclassical analysis, using fine properties of the quantum relative entropy, the link between quantum de Finetti measures and upper/lower symbols in a coherent state basis, as well as Berezin-Lieb type inequalities. Our results cover the measure built on the defocusing nonlinear Schr{\\"o}dinger functional on a finite interval, as well as smoother interactions in dimensions d\\textgreater{}1.
Many-body localization transition in random quantum spin chains with long-range interactions
NASA Astrophysics Data System (ADS)
Moure, N.; Haas, S.; Kettemann, S.
2015-07-01
While there are well-established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many-body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power ?, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing ?. At ?c the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many-body localization transition in disordered antiferromagnetic spin chains with long-range interactions.
Guidoni, Leonardo
Ab Initio Geometry and Bright Excitation of Carotenoids: Quantum Monte Carlo and Many Body Green state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy and coupling with Qy of the chlorophyll.8-13 Measurements in several solvents have been reported
Fokker Planck equations for globally coupled many-body systems with time delays
NASA Astrophysics Data System (ADS)
Frank, T. D.; Beek, P. J.
2005-10-01
A Fokker-Planck description for globally coupled many-body systems with time delays was developed by integrating previously derived Fokker-Planck equations for many-body systems and for time-delayed systems. By means of the Fokker-Planck description developed, we examined the dependence of the variability of many-body systems on attractive coupling forces and time delays. For a fundamental class of systems exemplified by a time-delayed Shimizu-Yamada model for muscular contractions, we established that the variability is an invertible one-to-one mapping of coupling forces and time delays and that coupling forces and time delays have opposite effects on system variability, allowing time delays to annihilate the impact of coupling forces. Furthermore, we showed how variability measures could be used to determine coupling parameters and time delays from experimental data.
Cavity quantum electrodynamics with many-body states of a two-dimensional electron gas.
Smolka, Stephan; Wuester, Wolf; Haupt, Florian; Faelt, Stefan; Wegscheider, Werner; Imamoglu, Ataç
2014-10-17
Light-matter interaction has played a central role in understanding as well as engineering new states of matter. Reversible coupling of excitons and photons enabled groundbreaking results in condensation and superfluidity of nonequilibrium quasiparticles with a photonic component. We investigated such cavity-polaritons in the presence of a high-mobility two-dimensional electron gas, exhibiting strongly correlated phases. When the cavity was on resonance with the Fermi level, we observed previously unknown many-body physics associated with a dynamical hole-scattering potential. In finite magnetic fields, polaritons show distinct signatures of integer and fractional quantum Hall ground states. Our results lay the groundwork for probing nonequilibrium dynamics of quantum Hall states and exploiting the electron density dependence of polariton splitting so as to obtain ultrastrong optical nonlinearities. PMID:25278508
Hybrid quantum magnetism in circuit QED: from spin-photon waves to many-body spectroscopy.
Kurcz, Andreas; Bermudez, Alejandro; García-Ripoll, Juan José
2014-05-01
We introduce a model of quantum magnetism induced by the nonperturbative exchange of microwave photons between distant superconducting qubits. By interconnecting qubits and cavities, we obtain a spin-boson lattice model that exhibits a quantum phase transition where both qubits and cavities spontaneously polarize. We present a many-body ansatz that captures this phenomenon all the way, from a the perturbative dispersive regime where photons can be traced out, to the nonperturbative ultrastrong coupling regime where photons must be treated on the same footing as qubits. Our ansatz also reproduces the low-energy excitations, which are described by hybridized spin-photon quasiparticles, and can be probed spectroscopically from transmission experiments in circuit QED, as shown by simulating a possible experiment by matrix-product-state methods. PMID:24856680
Probing many-body quantum states in single InAs quantum dots: Terahertz and tunneling spectroscopy
NASA Astrophysics Data System (ADS)
Zhang, Y.; Shibata, K.; Nagai, N.; Ndebeka-Bandou, C.; Bastard, G.; Hirakawa, K.
2015-06-01
We have investigated the many-body quantum states in single InAs quantum dots (QDs) by simultaneously obtaining the terahertz (THz) intersublevel transition and single electron tunneling spectra. It is found that the intersublevel transition energies measured in the few-electron region are systematically larger than the excited state (ES) energies determined from the transport measurements. We show that tunneling and THz spectroscopy probe the same many-body excited states in the QDs, but their sensitivities depend on their selection rules. In the many-electron region, we observe THz peaks whose energies coincide with the tunneling ESs.
Code C# for chaos analysis of relativistic many-body systems
I. V. Grossu; C. Besliu; Al. Jipa; D. Felea; C. C. Bordeianu; E. Stan; T. Esanu
2010-03-16
This work presents a new Microsoft Visual C# .NET code library, conceived as a general object oriented solution for chaos analysis of three-dimensional, relativistic many-body systems. In this context, we implemented the Lyapunov exponent and the "fragmentation level" (defined using the graph theory and the Shannon entropy). Inspired by existing studies on billiard nuclear models and clusters of galaxies, we tried to apply the virial theorem for a simplified many-body system composed by nucleons. A possible application of the "virial coefficient" to the stability analysis of chaotic systems is also discussed.
Generation of many-body entanglement in long-range interacting systems
NASA Astrophysics Data System (ADS)
Foss-Feig, Michael; Gong, Zhe-Xuan; Gorshkov, Alexey; Clark, Charles
2014-03-01
The existence of long-ranged interactions generally complicates the description of many-body systems. However, in the limit where the interactions become infinitely long-ranged--i.e. independent of distance--the emergence of extra conserved quantities typically makes the behavior quite simple. Such infinite-ranged interactions are often assumed in the description of experiments aiming to produce large scale entangled states, for instance via spin-squeezing, but of course ``infinite'' in this context is an idealization. We consider the generation of entanglement in Ising models with long (but not infinite) ranged interactions, which are relevant to the description of a variety of quantum information/simulation platforms including trapped ions, polar molecules, Rydberg atoms, and nitrogen vacancy centers in diamond. We demonstrate that there exists a notion of sufficiently long-ranged interactions, for which the scaling of entanglement with system size expected from the infinite-range idealization is completely unmodified. Our results have direct applications to experimental protocols aiming to achieve quantum-enhanced metrology.
Exponential Orthogonality Catastrophe in Single-particle and Many-body Localized Systems
Dong-Ling Deng; J. H. Pixley; Xiaopeng Li; S. Das Sarma
2015-08-06
We investigate the statistical orthogonality catastrophe (SOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the SOC gives rise to a wave function overlap between the pre- and post-quench ground states that has an exponential decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe. This exponential decay arises from a statistical charge transfer process where a particle can be effectively "transported" to an arbitrary lattice site. In a many-body localized phase, we find this non-local transport and the associated exponential SOC phenomenon to persist in the presence of interaction effects. We discuss possibilities of observing this "stronger" exponential SOC in cold atoms and mesoscopic systems.
Kaiser, Robin
Experimental observation of a phase transition in the evolution of many-body systems with dipolar (Dated:) Non-equilibrium dynamics of many-body systems is important in many branches of science effectively model the non-equilibrium dynamics of complex many-body systems, such as 3D spin
Diabatic ramping spectroscopy of many-body excited states for trapped-ion quantum simulators
B. Yoshimura; W. C. Campbell; J. K. Freericks
2014-02-28
Due to the experimental time constraints of state of the art quantum simulations with trapped ions, the direct preparation of the ground state by adiabatically ramping the field of a transverse field Ising model becomes more and more difficult as the number of particles increase. We propose a spectroscopy protocol that intentionally creates excitations through diabatic ramping of the transverse field and measures a low-noise observable as a function of time for a constant field to reveal the structure of the coherent dynamics of the resulting many-body states. To simulate the experimental data, noise from counting statistics and decoherence error are added. Compressive sensing is then applied to Fourier transform the simulated data into the frequency domain and extract the the low-lying energy excitation spectrum. By using compressive sensing, the amount of data in time needed to extract this energy spectrum is sharply reduced making such experiments feasible with current technology.
Electrostatically Embedded Many-Body Expansion for Large Systems, with Applications
Truhlar, Donald G
Electrostatically Embedded Many-Body Expansion for Large Systems, with Applications to Water present electrostatically embedded two-body and three-body expansions for calculating the energies of molecular clusters. The system is divided into fragments, and dimers or trimers of fragments are calculated
More many-body perturbation theory for an electron-ion system
Baker, G.A. Jr.; Johnson, J.D.
1997-10-01
From previous finite-temperature, quantum, many-body perturbation theory results for the grand partition function of an electron-ion fluid through order {epsilon}{sup 4}, we compute the electron and ion fugacities in terms of the volume per ion and the temperature to that same order in perturbation theory. From these results we also give the pressure, again to the same order in perturbation theory about the values for the non-interacting fluid.
Long-distance entanglement in many-body atomic and optical systems
Salvatore M. Giampaolo; Fabrizio Illuminati
2009-11-21
We discuss the phenomenon of long-distance entanglement in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate different patterns of site-dependent interaction couplings, singling out two general settings: Patterns that allow for perfect long-distance entanglement (LDE) in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi long-distance entanglement (QLDE) in the ground state of the system, namely, such such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
Pablo R. Zangara; Denise Bendersky; Horacio M. Pastawski
2015-02-22
We address the question on how weak perturbations, that are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by non reversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed $N$ spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as $ N $ increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.
NASA Astrophysics Data System (ADS)
Zangara, Pablo R.; Bendersky, Denise; Pastawski, Horacio M.
2015-04-01
We address the question of how weak perturbations, which are quite ineffective in small many-body systems, can lead to decoherence and hence to irreversibility when they proliferate as the system size increases. This question is at the heart of solid-state NMR. There, an initially local polarization spreads all over due to spin-spin interactions that conserve the total spin projection, leading to an equilibration of the polarization. In principle, this quantum dynamics can be reversed by changing the sign of the Hamiltonian. However, the reversal is usually perturbed by nonreversible interactions that act as a decoherence source. The fraction of the local excitation recovered defines the Loschmidt echo (LE), here evaluated in a series of closed N spin systems with all-to-all interactions. The most remarkable regime of the LE decay occurs when the perturbation induces proliferated effective interactions. We show that if this perturbation exceeds some lower bound, the decay is ruled by an effective Fermi golden rule (FGR). Such a lower bound shrinks as N increases, becoming the leading mechanism for LE decay in the thermodynamic limit. Once the polarization stayed equilibrated longer than the FGR time, it remains equilibrated in spite of the reversal procedure.
Landau-Zener transitions in noisy environments and in many-body systems
NASA Astrophysics Data System (ADS)
Sun, Deqiang
This dissertation discusses the Landau-Zener (LZ) theory and its application in noisy environments and in many-body systems. The first project considers the effect of fast quantum noise on LZ transitions. There are two important time intervals separated by the characteristic LZ time. For each interval we derive and solve the evolution equation, and match the solutions at the boundaries to get a complete solution. Outside the LZ time interval, we derive the master equation, which differs from the classical equation by a quantum commutation term. Inside the LZ time interval, the mixed longitudinal-transverse noise correlation renormalizes the LZ gap and the system evolves according to the renormalized LZ gap. In the extreme quantum regime at zero temperature our theory gives a beautiful result which coincides with that of other authors. Our initial attempts to solve two experimental puzzles - an isotope effect and the quantized hysteresis curve of a single molecular magnet - are also discussed. The second project considers an ultracold dilute Fermi gas in a magnetic field sweeping across the broad Feshbach resonance. The broad resonance condition allows us to use the single mode approximation and to neglect the energy dispersion of the fermions. We then propose the Global Spin Model Hamiltonian, whose ground state we solve exactly, which yields the static limit properties of the BEC-BCS crossover. We also study the dynamics of the Global Spin Model by converting it to a LZ problem. The resulting molecular production from the initial fermions is described by a LZ-like formula with a strongly renormalized LZ gap that is independent of the initial fermion density. We predict that molecular production during a field-sweep strongly depends on the initial value of magnetic field. We predict that in the inverse process of molecular dissociation, immediately after the sweeping stops there appear Cooper pairs with parallel electronic spins and opposite momenta.
Code C# for chaos analysis of relativistic many-body systems
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Felea, D.; Stan, E.; Esanu, T.
2010-08-01
This work presents a new Microsoft Visual C# .NET code library, conceived as a general object oriented solution for chaos analysis of three-dimensional, relativistic many-body systems. In this context, we implemented the Lyapunov exponent and the “fragmentation level” (defined using the graph theory and the Shannon entropy). Inspired by existing studies on billiard nuclear models and clusters of galaxies, we tried to apply the virial theorem for a simplified many-body system composed by nucleons. A possible application of the “virial coefficient” to the stability analysis of chaotic systems is also discussed. Catalogue identifier: AEGH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 30?053 No. of bytes in distributed program, including test data, etc.: 801?258 Distribution format: tar.gz Programming language: Visual C# .NET 2005 Computer: PC Operating system: .Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread RAM: 128 Megabytes Classification: 6.2, 6.5 External routines: .Net Framework 2.0 Library Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, and energy conservation precision test. Additional comments: Easy copy/paste based deployment method. Running time: Quadratic complexity.
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Felea, D.; Esanu, T.; Stan, E.; Bordeianu, C. C.
2013-04-01
In this paper we present a new version of the Chaos Many-Body Engine C# application (Grossu et al. 2012 [1]). In order to benefit from the latest technological advantages, we migrated the application from .Net Framework 2.0 to .Net Framework 4.0. New tools were implemented also. Trying to estimate the particle interactions dependence on initial conditions, we considered a new distance, which takes into account only the structural differences between two systems. We used this distance for implementing the “Structural Lyapunov” function. We propose also a new precision test based on temporal reversed simulations. New version program summaryProgram title: Chaos Many-Body Engine v03 Catalogue identifier: AEGH_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGH_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 214429 No. of bytes in distributed program, including test data, etc.: 9512380 Distribution format: tar.gz Programming language: Visual C# .Net 2010 Computer: PC Operating system: .Net Framework 4.0 running on MS Windows RAM: 128 MB Classification: 24.60.Lz, 05.45.a Catalogue identifier of previous version: AEGH_v2_0 Journal reference of previous version: Computer Physics Communications 183 (2012) 1055-1059 Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm. Implementation of temporal reversed simulation precision test, and “Structural Lyapunov” function. In order to benefit from the advantages involved in the latest technologies (e.g. LINQ Queries [2]), Chaos Many-Body Engine was migrated from .Net Framework 2.0 to .Net Framework 4.0. In addition to existing energy conservation assessment [3], we propose also a reverse simulation precision test. Thus, for a regular simulation, we considered the corresponding reversed process: initial time equals the end time of regular simulation, and temporal resolution dt<0. One can compare the initial state of the regular system, and the final state of the reversed one (t=0) using, for example, the phase-space distance. Trying to measure particle interactions dependence on initial conditions, we considered the following distance, which takes into account only the structure differences between two many-body systems with reactions: ds=?{?i=1n where Ni1 represents the number of particles of type “i” from the first system, and Ni2 is the corresponding number for the second system. We sum over all particle types. Inspired by the Lyapunov Exponent method [4], we implemented the evolution in time of the “Structural Lyapunov” function, for two identical systems with slightly different initial conditions: Ls(t)=ln ds(t)/ds(0). Migration from .Net Framework 2.0 to .Net Framework 4.0 Reverse simulation precision test “Structural Lyapunov” function. In [1] we applied the Chaos Many-Body Engine to some nuclear relativistic collisions at 4.5 A GeV/c (SKM 200 collaboration [5,6]). We considered also some first tests on He+He head-on collisions at 1 A TeV/c (choose the Simulation?Collision menu, and set the appropriate parameters Fig. 1). However, in this case, more complex reaction schemas should be considered. Further investigation on higher energies is currently in progress. He+He central, head-on collision at 1 A TeV/c (example of use). Restrictions: The reverse simulation precision test does not apply for: systems with reactions, parallel simulations, and Monte Carlo simulations. Running time: quadratic complexity.
Renormalization of myoglobin-ligand binding energetics by quantum many-body effects.
Weber, Cédric; Cole, Daniel J; O'Regan, David D; Payne, Mike C
2014-04-22
We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory. This combination of methods explicitly accounts for dynamical and multireference quantum physics, such as valence and spin fluctuations, of the 3d electrons, while treating a significant proportion of the protein (more than 1,000 atoms) with DFT. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long-standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a strong imbalance between O2 and CO binding, favoring the latter to an unphysically large extent. We show that the explicit inclusion of the many-body effects induced by the Hund's coupling mechanism results in the correct prediction of similar binding energies for oxy- and carbonmonoxymyoglobin. PMID:24717844
Schreiber, Michael; Hodgman, Sean S; Bordia, Pranjal; Lüschen, Henrik P; Fischer, Mark H; Vosk, Ronen; Altman, Ehud; Schneider, Ulrich; Bloch, Immanuel
2015-08-21
Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions. PMID:26229112
Nonperturbative Renormalisation Group: Applications to the few and many-body systems
B. Krippa
2009-12-18
We consider the applications of functional renormalisation group to few and many-body systems. As an application to the few-body dynamics we study the ratio between the fermion-fermion scattering length and the dimer-dimer scattering length for systems of few nonrelativistic fermions. We find a strong dependence on the cutoff function used in the renormalisation flow for a two-body truncation of the action. Adding a simple three-body term substantially reduces this dependence. In the context of many-body physics we study the dynamics of both symmetric and asymmetric many-fermion systems using the same functional renormalisation technique. It is demonstrated that functional renormalisation group gives sensible and reliable results and provides a solid theoretical ground for the future studies. Open questions as well as lines of further developments are discussed.
A monomial matrix formalism to describe quantum many-body states
NASA Astrophysics Data System (ADS)
Van den Nest, Maarten
2011-12-01
We propose a framework to describe and simulate a class of many-body quantum states. We do so by considering joint eigenspaces of sets of monomial unitary matrices, called here ‘M-spaces’ a unitary matrix is monomial if precisely one entry per row and column is nonzero. We show that M-spaces encompass various important state families, such as all Pauli stabilizer states and codes, the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, Kitaev's (Abelian and non-Abelian) anyon models, group coset states, W states and the locally maximally entanglable states. We furthermore show how basic properties of M-spaces can be understood transparently by manipulating their monomial stabilizer groups. In particular, we derive a unified procedure to construct an eigenbasis of any M-space, yielding an explicit formula for each of the eigenstates. We also discuss the computational complexity of M-spaces and show that basic problems, such as estimating local expectation values, are NP-hard. Finally, we prove that a large subclass of M-spaces—containing, in particular, most of the aforementioned examples—can be simulated efficiently classically with a unified method.
Caballero-Benitez, Santiago F
2015-01-01
Quantum trapping potentials for ultracold gases change the landscape of classical properties of scattered light and matter. The atoms in a quantum many-body correlated phase of matter change the properties of light and vice versa. The properties of both light and matter can be tuned by design and depend on the interplay between long-range (nonlocal) interactions mediated by an optical cavity and short-range processes of the atoms. Moreover, the quantum properties of light get significantly altered by this interplay, leading the light to have nonclassical features. Further, these nonclassical features can be designed and optimised.
Code C# for chaos analysis of relativistic many-body systems with reactions
NASA Astrophysics Data System (ADS)
Grossu, I. V.; Besliu, C.; Jipa, Al.; Stan, E.; Esanu, T.; Felea, D.; Bordeianu, C. C.
2012-04-01
In this work we present a reaction module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross section, particle lifetime, etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincaré section, we propose also the “Clusterization Map”, as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 Collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular ? distributions. Catalogue identifier: AEGH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 184 628 No. of bytes in distributed program, including test data, etc.: 7 905 425 Distribution format: tar.gz Programming language: Visual C#.NET 2005 Computer: PC Operating system: Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread. One processor used for each many-body system. RAM: 128 Megabytes Classification: 6.2, 6.5 Catalogue identifier of previous version: AEGH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1464 External routines: Net Framework 2.0 Library Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems with reactions. Object oriented solution, easy to reuse, extend and customize, in any development environment which accepts .Net assemblies or COM components. Treatment of two particles reactions and decays. For each particle, calculation of the time measured in the particle reference frame, according to the instantaneous velocity. Possibility to dynamically add particle properties (spin, isospin, etc.), and reactions/decays, using a specific XML input file. Basic support for Monte Carlo simulations. Implementation of: Lyapunov exponent, “fragmentation level”, “average system radius”, “virial coefficient”, “clusterization map”, and energy conservation precision test. As an example of use, we implemented a toy-model for nuclear relativistic collisions at 4.5 A GeV/c. Reasons for new version: Following our goal of applying chaos theory to nuclear relativistic collisions at 4.5 A GeV/c, we developed a reaction module integrated with the Chaos Many-Body Engine. In the previous version, inheriting the Particle class was the only possibility of implementing more particle properties (spin, isospin, and so on). In the new version, particle properties can be dynamically added using a dictionary object. The application was improved in order to calculate the time measured in the own reference frame of each particle. two particles reactions: a+b?c+d, decays: a?c+d, stimulated decays, more complicated schemas, implemented as various combinations of previous reactions. Following our goal of creating a flexible application, the reactions list, including the corresponding properties (cross sections, particles lifetime, etc.), could be supplied as parameter, using a specific XML configuration file. The simulation output files were modified for systems with reactions, assuring also the backward compatibility. We propose the “Clusterization Map” as a new investigation method of many-body systems. The multi-dimensional Lyapunov Exponent was adapted in order to be used for systems with variable structure. Basic support for Monte Carlo simulations was also added. Additiona
Morphology of Laplacian growth processes and statistics of equivalent many-body systems
Blumenfeld, R.
1994-11-01
The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes.
Formation of fractal structure in many-body systems with attractive power-law potentials
Hiroko Koyama; Tetsuro Konishi
2005-12-13
We study the formation of fractal structure in one-dimensional many-body systems with attractive power-law potentials. Numerical analysis shows that the range of the index of the power for which fractal structure emerges is limited. Dependence of the growth rate on wavenumber and power-index is obtained by linear analysis of the collisionless Boltzmann equation, which supports the numerical results.
Yi-Zhuang You; Xiao-Liang Qi; Cenke Xu
2015-08-14
We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the $1d$ interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.
Code C# for chaos analysis of relativistic many-body systems with reactions
I. V. Grossu; C. Besliu; Al. Jipa; E. Stan; T. Esanu; D. Felea; C. C. Bordeianu
2010-09-11
In this work we present a reactions module for "Chaos Many-Body Engine" (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross-section, particles lifetime etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincare section, we propose also the "Clusterization map", as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular {\\pi}- distributions.
Gonzalo A. Alvarez; Dieter Suter; Robin Kaiser
2014-09-16
Non-equilibrium dynamics of many-body systems is important in many branches of science, such as condensed matter, quantum chemistry, and ultracold atoms. Here we report the experimental observation of a phase transition of the quantum coherent dynamics of a 3D many-spin system with dipolar interactions, and determine its critical exponents. Using nuclear magnetic resonance (NMR) on a solid-state system of spins at room-temperature, we quench the interaction Hamiltonian to drive the evolution of the system. The resulting dynamics of the system coherence can be localized or extended, depending on the quench strength. Applying a finite-time scaling analysis to the observed time-evolution of the number of correlated spins, we extract the critical exponents v = s = 0.42 around the phase transition separating a localized from a delocalized dynamical regime. These results show clearly that such nuclear-spin based quantum simulations can effectively model the non-equilibrium dynamics of complex many-body systems, such as 3D spin-networks with dipolar interactions.
Chaos in fermionic many-body systems and the metal-insulator transition
T. Papenbrock; Z. Pluhar; J. Tithof; H. A. Weidenmueller
2011-02-07
We show that finite Fermi systems governed by a mean field and a few-body interaction generically possess spectral fluctuations of the Wigner-Dyson type and are, thus, chaotic. Our argument is based on an analogy to the metal-insulator transition. We construct a sparse random-matrix ensemble ScE that mimics that transition. Our claim then follows from the fact that the generic random-matrix ensemble modeling a fermionic interacting many-body system is much less sparse than ScE.
Spreading in Integrable and Non--integrable Many--body Systems
Johannes Freese; Boris Gutkin; Thomas Guhr
2014-09-19
We consider a finite, closed and selfbound many--body system in which a collective degree of freedom is excited. The redistribution of energy and momentum into the non--collective degrees of freedom is referred to as spreading. Thus, spreading closely relates to thermalization. We carry out numerical simulations to show that spreading can be present and absent in integrable systems. Consequently, non--integrability is not a necessary condition for spreading. We identify subtle features which determine the onset of spreading. We also compare with a non--integrable case.
Calculation of local pressure tensors in systems with many-body interactions
Hendrik Heinz; Wolfgang Paul; Kurt Binder
2006-02-24
Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4, . . .) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infinitesimal areas. To define dissection by a small area, respective n-body interactions are divided into two geometric centers, effectively reducing them to two-body interactions. Consistency with hydrodynamics-derived formulas for systems with two-body interactions (J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)), for average cross-sectional pressures (B. D. Todd, D. J. Evans, and P. J. Daivis, Phys. Rev. E 52, 1627 (1995)), and for volume averaged pressures (virial formula) is shown. As a simple numerical example, we discuss liquid propane in a cubic box. Local, crosssectional,and volume-averaged pressures as well as relative contributions from two-body and three-body forces are analyzed with the proposed method, showing full numerical equivalence with the existing approaches. The method allows computing local pressures in the presence of many-body interactions in atomistic simulations of complex materials and biological systems.
Many-body systems in the presence of the random interaction and the $J$ pairing interaction
A. Arima
2004-05-26
In this talk I shall discuss some regularities of many-body systems in the presence of random interactions and regularities of a single-$j$ shell for the $J$ pairing interaction which works only when two particles are coupled to spin $J$. I shall first explain an empirical rule to predict the spin $I$ ground state probability. Then I shall present some interesting results of a single-$j$ shell under the $J$ pairing interaction. Last I shall discuss some preliminary results of binding energies in the presence of random two-body interactions.
Exponential series expansion for correlation functions of many-body systems
NASA Astrophysics Data System (ADS)
Barocchi, Fabrizio; Guarini, Eleonora; Bafile, Ubaldo
2014-09-01
We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function c (t) can always be expanded in a series of (complex) exponential functions of time when its Laplace transform C˜(z) has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades. Our method is based on a different projection technique in the Hilbert space S of the system and shows that appropriate approximations of the exponential series are related to the contraction of S to a finite, usually small, number of dimensions. The time dependence of correlation functions is always described in detail by a multiple-exponential functionality also at long times. This result is therefore also valid for correlation functions of many-body Hamiltonian systems for which a power-law dependence, observed in restricted time ranges and predicted to be the asymptotic one, can be considered at most as a useful approximate modeling of long-time behavior.
Exponential series expansion for correlation functions of many-body systems.
Barocchi, Fabrizio; Guarini, Eleonora; Bafile, Ubaldo
2014-09-01
We demonstrate that in Hamiltonian many-body systems at equilibrium, any kind of time dependent correlation function c(t) can always be expanded in a series of (complex) exponential functions of time when its Laplace transform C?(z) has single poles. The characteristic frequencies can be identified as the eigenfrequencies of the correlation. This is done without introducing the concepts of fluctuating forces and memory functions, due to Mori and Zwanzig and extensively used in the literature in the last decades. Our method is based on a different projection technique in the Hilbert space S of the system and shows that appropriate approximations of the exponential series are related to the contraction of S to a finite, usually small, number of dimensions. The time dependence of correlation functions is always described in detail by a multiple-exponential functionality also at long times. This result is therefore also valid for correlation functions of many-body Hamiltonian systems for which a power-law dependence, observed in restricted time ranges and predicted to be the asymptotic one, can be considered at most as a useful approximate modeling of long-time behavior. PMID:25314394
Quantum quenches and many-body localization in the thermodynamic limit
NASA Astrophysics Data System (ADS)
Tang, Baoming; Iyer, Deepak; Rigol, Marcos
2015-04-01
We use thermalization indicators and numerical linked cluster expansions to probe the onset of many-body localization in a disordered one-dimensional hard-core boson model in the thermodynamic limit. We show that after equilibration following a quench from a delocalized state, the momentum distribution indicates a freezing of one-particle correlations at higher values than in thermal equilibrium. The position of the delocalization to localization transition, identified by the breakdown of thermalization with increasing disorder strength, is found to be consistent with the value from the level statistics obtained via full exact diagonalization of finite chains. Our results strongly support the existence of a many-body localized phase in the thermodynamic limit.
Lea F. Santos; Fausto Borgonovi; Giuseppe Luca Celardo
2015-07-23
We study the dynamics of many-body quantum spin-$1/2$ systems with long-range interaction, as the ones recently realized with trapped ions. Our analysis reveals a scenario that is richer than the usual expectation that interactions of longer range should necessarily lead to faster dynamics. Long-range interaction induces superselection rules that become exact in the thermodynamic limit. They confine the dynamics to invariant subspaces, which are shielded from the long-range interaction. Consequently, the evolution may even freeze as the system size increases. We establish an analogy between this effective shielding and the onset of quantum Zeno subspaces, with the difference that here they are driven by system size, instead of interaction strength.
Long-range interacting many-body systems with alkaline-earth-metal atoms
B. Olmos; D. Yu; Y. Singh; F. Schreck; K. Bongs; I. Lesanovsky
2013-04-11
Alkaline-earth-metal atoms exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the 3P_0-3D_1-transition of the triplet manifold. In case of bosonic strontium, which we discuss here, this transition has a wavelength of 2.7 \\mu m and a dipole moment of 2.46 Debye, and there exists a magic wavelength permitting the creation of optical lattices that are identical for the states 3P_0 and 3D_1. This interaction enables the realization and study of mixtures of hard-core lattice bosons featuring long-range hopping, with tuneable disorder and anisotropy. We derive the many-body Master equation, investigate the dynamics of excitation transport and analyze spectroscopic signatures stemming from coherent long-range interactions and collective dissipation. Our results show that lattice gases of alkaline-earth-metal atoms permit the creation of long-lived collective atomic states and constitute a simple and versatile platform for the exploration of many-body systems with long-range interactions. As such, they represent an alternative to current related efforts employing Rydberg gases, atoms with large magnetic moment, or polar molecules.
Quantum many-body models with cold atoms coupled to photonic crystals
J. S. Douglas; H. Habibian; C. -L. Hung; A. V. Gorshkov; H. J. Kimble; D. E. Chang
2015-02-28
Using cold atoms to simulate strongly interacting quantum systems represents an exciting frontier of physics. However, achieving tunable, coherent long-range interactions between atoms is an outstanding challenge, which currently leaves a large class of models inaccessible to quantum simulation. Here, we propose a solution exploiting the powerful new platform of cold atoms trapped near nano-photonic systems. We show that the dielectric contrast of an atom trapped near a photonic crystal can seed a localized cavity mode around the atomic position. In a dynamic form of "all-atomic" cavity QED, the length of these cavity modes can be tuned, and atoms separated by the order of the effective cavity length can interact coherently with each other. Considering realistic conditions such as fabrication disorder and photon losses, coherent long-range potentials or spin interactions can be dominant in the system over length scales up to hundreds of wavelengths.
Quantum many-body models with cold atoms coupled to photonic crystals
NASA Astrophysics Data System (ADS)
Douglas, J. S.; Habibian, H.; Hung, C.-L.; Gorshkov, A. V.; Kimble, H. J.; Chang, D. E.
2015-05-01
Using cold atoms to simulate strongly interacting quantum systems is an exciting frontier of physics. However, because atoms are nominally neutral point particles, this limits the types of interaction that can be produced. We propose to use the powerful new platform of cold atoms trapped near nanophotonic systems to extend these limits, enabling a novel quantum material in which atomic spin degrees of freedom, motion and photons strongly couple over long distances. In this system, an atom trapped near a photonic crystal seeds a localized, tunable cavity mode around the atomic position. We find that this effective cavity facilitates interactions with other atoms within the cavity length, in a way that can be made robust against realistic imperfections. Finally, we show that such phenomena should be accessible using one-dimensional photonic crystal waveguides in which coupling to atoms has already been experimentally demonstrated.
Many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid theory
NASA Astrophysics Data System (ADS)
Arakawa, Naoya
2015-06-01
I review many-body effects on the resistivity of a multi-orbital system beyond Landau's Fermi-liquid (FL) theory. Landau's FL theory succeeds in describing electronic properties of some correlated electron systems at low temperatures. However, the behaviors deviating from the temperature dependence in the FL, non-FL-like behaviors, emerge near a magnetic quantum-critical point (QCP). These indicate the importance of many-body effects beyond Landau's FL theory. Those effects in multi-orbital systems have been little understood, although their understanding is important to deduce ubiquitous properties of correlated electron systems and characteristic properties of multi-orbital systems. To improve this situation, I formulate the resistivity of a multi-orbital Hubbard model using the extended Éliashberg theory and adopt this method to the inplane resistivity of quasi-two-dimensional paramagnetic ruthenates in combination with the fluctuation-exchange approximation including the current vertex corrections arising from the self-energy and Maki-Thompson term. The results away from and near the antiferromagnetic QCP reproduce the temperature dependence observed in Sr2RuO4 and Sr2Ru0.075Ti0.025O4, respectively. I highlight the importance of not only the momentum and the temperature dependence of the damping of a quasiparticle but also its orbital dependence in discussing the resistivity of correlated electron systems.
Kondo Physics and Many-Body Effects in Quantum Dots and Molecular Junctions
NASA Astrophysics Data System (ADS)
Ruiz-Tijerina, David A.
In this document we present a study of the thermodynamic and transport properties of two kinds of quantum impurity systems in the Kondo regime. The first system consists of a spin-1 molecule in which mechanical stretching along the transport axis produces a magnetic anisotropy. We find that a generic coupling between a vibrational mode along this axis and the molecular spin induces a correction to the magnetic anisotropy, driving the ground state of the system into a non-Fermi-liquid phase. A transition into a Fermi-liquid ground state can then be induced by means of stretching, going through an underscreened spin-1 Kondo ground state at zero effective anisotropy. In the second system we study the effects of a charge detector, implemented by a quantum point-contact (QPC), on the Kondo state of a nearby spin-1/2 quantum dot (QD). While making the charge detection possible, the Coulomb interaction between the electrons traversing the QPC and those within the QD contribute to decoherence of the Kondo state. By modeling the QPC as two metallic terminals connected to an intermediate localized level, we can explore three transport regimes of the detector: a zero-conductance regime, a finite-conductance regime in mixed valence, and unitary conductance in a Kondo ground state that has been suggested as an explanation to the "0.7 anomaly" in QPCs. Transitions between these different ground states can be achieved by tuning the strength of a capacitive coupling that parameterizes the electrostatic interaction.
Paradoxical probabilistic behavior for strongly correlated many-body classical systems
NASA Astrophysics Data System (ADS)
Jauregui, Max; Tsallis, Constantino
2015-09-01
Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that each row is a list of n strongly correlated random variables. The correlations are preserved even when n ? ?, since the standard central limit theorem does not hold for this array. We show that, if we choose a fixed number m < n of random variables of the nth row and trace over the other n - m variables, and then consider n ? ?, the m chosen ones can, paradoxically, turn out to be independent. However, the scenario can be different if m increases with n. Finally, we suggest a possible experimental verification of our results near criticality of a second-order phase transition.
Paradoxical probabilistic behavior for strongly correlated many-body classical systems
Max Jauregui; Constantino Tsallis
2015-02-02
Using a simple probabilistic model, we illustrate that a small part of a strongly correlated many-body classical system can show a paradoxical behavior, namely asymptotic stochastic independence. We consider a triangular array such that each row is a list of $n$ strongly correlated random variables. The correlations are preserved even when $n\\to\\infty$, since the standard central limit theorem does not hold for this array. We show that, if we choose a fixed number $mvariables of the $n$th row and trace over the other $n-m$ variables, and then consider $n\\to\\infty$, the $m$ chosen ones can, paradoxically, turn out to be independent. However, the scenario can be different if $m$ increases with $n$. Finally, we suggest a possible experimental verification of our results near criticality of a second-order phase transition.
Scaling Limit and Renormalisation Group in General (Quantum) Many Body Theory
Manfred Requardt
2001-08-30
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation group analysis of the critical regime. The approach is completely general, encompassing classical, quantum, discrete and continuous systems. Our central theme is the analysis of the famous `scaling hypothesis', that is, we make a general investigation under what cluster conditions of the l-point correlation functions a scale invariant (non-trivial) limit theory can be actually attained.
Many-Body Quantum Chemistry for the Electron Gas: Convergent Perturbative Theories
NASA Astrophysics Data System (ADS)
Shepherd, James J.; Grüneis, Andreas
2013-05-01
We investigate the accuracy of a number of wave function based methods at the heart of quantum chemistry for metallic systems. Using the Hartree-Fock wave function as a reference, perturbative (Møller-Plesset) and coupled cluster theories are used to study the uniform electron gas model. Our findings suggest that nonperturbative coupled cluster theories are acceptable for modeling electronic interactions in metals while perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely used coupled cluster singles and doubles plus perturbative triples method that lifts the divergent behavior and is shown to give very accurate correlation energies for the homogeneous electron gas.
Quantum many-body theory for qubit decoherence in a finite-size spin bath
Yang Wen; Liu Renbao
2008-11-07
We develop a cluster-correlation expansion theory for the many-body dynamics of a finite-size spin bath in a time scale relevant to the decoherence of a center spin or qubit embedded in the bath. By introducing the cluster correlation as the evolution of a group of bath spins divided by the correlations of all the subgroups, the propagator of the whole bath is factorized into the product of all possible cluster correlations. Each cluster-correlation term accounts for the authentic (non-factorizable) collective excitations within that group. Convergent results can be obtained by truncating the cluster-correlation expansion up to a certain cluster size, as verified in an exactly solvable spin-chain model.
Nuclear quantum many-body dynamics. From collective vibrations to heavy-ion collisions
NASA Astrophysics Data System (ADS)
Simenel, Cédric
2012-11-01
A summary of recent researches on nuclear dynamics with realistic microscopic quantum approaches is presented. The Balian-Vénéroni variational principle is used to derive the time-dependent Hartree-Fock (TDHF) equation describing the dynamics at the mean-field level, as well as an extension including small-amplitude quantum fluctuations which is equivalent to the time-dependent random-phase approximation (TDRPA). Such formalisms as well as their practical implementation in the nuclear physics framework with modern three-dimensional codes are discussed. Recent applications to nuclear dynamics, from collective vibrations to heavy-ion collisions are presented. Particular attention is devoted to the interplay between collective motions and internal degrees of freedom. For instance, the harmonic nature of collective vibrations is questioned. Nuclei are also known to exhibit superfluidity due to pairing residual interaction. Extensions of the theoretical approach to study such pairing vibrations are now available. Large amplitude collective motions are investigated in the framework of heavy-ion collisions leading, for instance, to the formation of a compound system. How fusion is affected by the internal structure of the collision partners, such as their deformation, is discussed. Other mechanisms in competition with fusion, and responsible for the formation of fragments which differ from the entrance channel (transfer reactions, deep-inelastic collisions, and quasi-fission) are investigated. Finally, studies of actinide collisions forming, during very short times of few zeptoseconds, the heaviest nuclear systems available on Earth, are presented.
Stability and Clustering for Lattice Many-Body Quantum Hamiltonians with Multiparticle Potentials
NASA Astrophysics Data System (ADS)
Faria da Veiga, Paulo A.; O'Carroll, Michael
2015-08-01
We analyze a quantum system of N identical spinless particles of mass m, in the lattice Z^d , given by a Hamiltonian H_N=T_N+V_N , with kinetic energy T_N?0 and potential V_N=V_{N,2}+V_{N,3} composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials V_{N,2} and V_{N,3} on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the H_N spectrum, \\underline{? }(H_N)? -cN , for c>0 independent of N. For V_{N,3}=0 , H_N is unstable, and the system collapses. If V_{N,3}not =0 , H_N is stable and, for strong enough repulsion, we obtain \\underline{? }(H_N)? -c' N , where c'N is the energy of (N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [ \\underline{? }(V_N)/N ] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value N_s of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers N_r and N_s-N_r , with N_r=1,ldots ,N_s-1.
Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
Xiaopeng Li; Sriram Ganeshan; J. H. Pixley; S. Das Sarma
2015-08-18
We investigate many body localization in the presence of a single particle mobility edge. By considering an interacting deterministic model with an incommensurate potential in one dimension we find that the single particle mobility edge in the noninteracting system leads to a many body mobility edge in the corresponding interacting system for certain parameter regimes. Using exact diagonalization, we probe the mobility edge via energy resolved entanglement entropy (EE) and study the energy resolved applicability (or failure) of the eigenstate thermalization hypothesis (ETH). Our numerical results indicate that the transition separating area and volume law scaling of the EE does not coincide with the non-thermal to thermal transition. Consequently, there exists an extended non-ergodic phase for an intermediate energy window where the many body eigenstates violate the ETH while manifesting volume law EE scaling. We also establish that the model possesses an infinite temperature many body localization transition despite the existence of a single particle mobility edge. We propose a practical scheme to test our predictions in atomic optical lattice experiments which can directly probe the effects of the mobility edge.
Vilkas, Marius J.; Ishikawa, Yasuyuki
2005-09-15
High-accuracy calculations of term energies and wavelengths of resonance lines in Zn-like ions have been performed as benchmarks in the quest for accurate theoretical treatments of relativity, electron correlation, and quantum electrodynamic effects in multivalence-electron systems. Computed wavelengths of the 4s{sup 2} {sup 1}S{sub 0}-4s4p {sup 1}P{sub 1}{sup o} transitions are compared with the recent high-resolution wavelength measurements using electron-beam ion traps [E. Traebert, P. Beiersdorfer, and H. Chen, Phys. Rev. A 70, 032506 (2004)], a sensitive means of testing electronic structure theory that has revealed the inadequacies in treating multiple valence electrons in the extant relativistic many-body calculations.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-06-01
A simple approach is discussed which associates to (solvable) matrix equations (solvable) dynamical systems, generally interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. We then focus on cases in which the auxiliary variables can be altogether eliminated, reobtaining thereby (via this unified approach) well-known solvable many-body problems, and moreover a (solvable) extension of the "goldfish" model.
NASA Astrophysics Data System (ADS)
Buot, F. A.
1990-12-01
A formal derivation of a generalized equation of a Wigner distribution function including all many-body effects and all scattering mechanisms is given. The result is given in integral operator form suitable for application to the numerical modeling of quantum tunneling and quantum interference solid state devices. In the absence of scattering and many-body effects, the result reduces to the "noninteracting-particle" Wigner distribution function equation, often used to simulate resonant tunneling devices. The derivation uses a Weyl transform technique which can easily incorporate Bloch electrons. Weyl transforms of self-energies are derived. Various simplifications of a general quantum transport equation for semiconductor device analysis and self-consistent numerical simulation of a quantum distribution function in the phase-space/frequency-time domain are discussed. Recent attempts to include collisions in the Wigner distribution-function approach to the numerical simulation of tunneling devices are clearly shown to be non-self-consistent and inaccurate; more accurate numerical simulation is needed for a deeper understanding of the effects of collision and scattering.
Many-body Physics in One-dimensional Ultra-cold Atomic Systems
NASA Astrophysics Data System (ADS)
Wei, Bobo
Over the last ten years or so, there have been a number of dramatic experimental developments in trapping, cooling and controlling atoms, which open up new opportunities for studying strongly interacting many-body systems. Cold atom systems are very clean and highly tunable. Systems with different dimensionalities can be realized through optical lattice confinement, and the interactions between atoms can be fine-tuned to any value desired by Feshbach resonance. In this way various simple models can be realized to analyze subtle many-body problems which are difficult to analyze because of the complexity of the systems in real materials. In the first part of the thesis, we investigate ground state properties of Tonks-Girardeau(TG) gas in an one-dimensional periodic trap. The key issue we are interested in is whether periodically-trapped TG gas has an off-diagonal long range order. Through numerical calculations, the single-particle reduced density matrix is computed for systems with up to 265 bosons. Scaling analysis on the occupation number of the lowest orbital shows that there is no Bose-Einstein condensation for the periodically-trapped TG gas in both commensurate and incommensurate cases. We find that, for the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, 0.5 and 1, respectively, while for the incommensurate case, they are 0.5, 0.5, and 1.5, respectively. These exponents are related to each other by a universal relation. In the second part we study the one-dimensional "hard-sphere" fermions and bosons systems. The pair distribution functions of the one-dimensional "hard-sphere" fermions and bosons systems have been exactly evaluated by introducing gap variables. Some interesting results are obtained. Meanwhile, the pair distribution function could be measured in experiments, so hopefully our numerical results may be observed experimentally in the near future. Lastly, we investigate the one-dimensional multi-component fermions and bosons systems. This is an extension of the work of C.N.Yang and Y.Z.You in 2011. Yang and You studied the ground state energy of w-component fermions and bosons with repulsive interactions. In this part, we investigate w-component fermions and bosons in an attractive interaction regime. Several theorems about the ground state energy of w-component fermions and bosons systems are stated and proved. Combing the results in the work of Yang and You, we finally have a comprehensive picture for the ground state energy of one-dimensional fermions and bosons systems.
Renormalization of myoglobin-ligand binding energetics by quantum many-body effects
Weber, Cedric; O'Regan, David D; Payne, Mike C
2014-01-01
We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory (DMFT). This combination of methods explicitly accounts for dynamical and multi-reference quantum physics, such as valence and spin fluctuations, of the 3d electrons, whilst treating a significant proportion of the protein (more than 1000 atoms) with density functional theory. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a st...
Efficient Implementation of Many-body Quantum Chemical Methods on the Intel Xeon Phi Coprocessor
Apra, Edoardo; Klemm, Michael; Kowalski, Karol
2014-12-01
This paper presents the implementation and performance of the highly accurate CCSD(T) quantum chemistry method on the Intel Xeon Phi coprocessor within the context of the NWChem computational chemistry package. The widespread use of highly correlated methods in electronic structure calculations is contingent upon the interplay between advances in theory and the possibility of utilizing the ever-growing computer power of emerging heterogeneous architectures. We discuss the design decisions of our implementation as well as the optimizations applied to the compute kernels and data transfers between host and coprocessor. We show the feasibility of adopting the Intel Many Integrated Core Architecture and the Intel Xeon Phi coprocessor for developing efficient computational chemistry modeling tools. Remarkable scalability is demonstrated by benchmarks. Our solution scales up to a total of 62560 cores with the concurrent utilization of Intel Xeon processors and Intel Xeon Phi coprocessors.
Hartono, Albert; Lu, Qingda; henretty, thomas; Krishnamoorthy, Sriram; zhang, huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-11-12
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.
Boal, David
PHYS415 Lecture 11 - Many-body systems: interacting 1 Â© 1996 by David Boal, Simon Fraser University or copying is strictly prohibited. #12;PHYS415 Lecture 11 - Many-body systems: interacting 3 Â© 1996 by David. #12;PHYS415 Lecture 11 - Many-body systems: interacting 4 Â© 1996 by David Boal, Simon Fraser
Philip Richerme; Crystal Senko; Jacob Smith; Aaron Lee; Simcha Korenblit; Christopher Monroe
2013-05-10
We use local adiabatic evolution to experimentally create and determine the ground state spin ordering of a fully-connected Ising model with up to 14 spins. Local adiabatic evolution -- in which the system evolution rate is a function of the instantaneous energy gap -- is found to maximize the ground state probability compared with other adiabatic methods while only requiring knowledge of the lowest $\\sim N$ of the $2^N$ Hamiltonian eigenvalues. We also demonstrate that the ground state ordering can be experimentally identified as the most probable of all possible spin configurations, even when the evolution is highly non-adiabatic.
Michal Svrcek
2010-08-24
We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the electron-vibrational Hamiltonian is fundamentally inconsistent with the Born-Handy ansatz so that such a treatment can never respect the COM problem. Born-Oppenheimer (B-O) approximation reveals some secret: it is a limit case where the degrees of freedom can be treated in a classical way. Beyond the B-O approximation they are inseparable in principle. The unique covariant description of all equations with respect to individual degrees of freedom leads to new types of interaction: besides the known vibronic (electron-phonon) one the rotonic (electron-roton) and translonic (electron-translon) interactions arise. We have proved that due to the COM problem only the hypervibrations (hyperphonons, i.e. phonons + rotons + translons) have true physical meaning in molecules and crystals; nevertheless, the use of pure vibrations (phonons) is justified only in the adiabatic systems. This fact calls for the total revision of our contemporary knowledge of all non-adiabatic effects, especially the Jahn-Teller effect and superconductivity. The vibronic coupling is responsible only for removing of electron (quasi)degeneracies but for the explanation of symmetry breaking and forming of structure the rotonic and translonic coupling is necessary.
NASA Astrophysics Data System (ADS)
Fischer, Uwe R.; Lode, Axel U. Â. J.; Chatterjee, Budhaditya
2015-06-01
The occupation of more than one single-particle state, and hence the emergence of fragmentation, is a many-body phenomenon occurring for systems of spatially confined strongly interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems in single wells. We solve the full many-body Schrödinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method (R-MCTDHB). The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density, and interaction strength is assessed. For contact interactions, it is found that the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long ranged the interactions become. At fixed particle number N , the degree of fragmentation is increasing when the density is decreasing, as expected in one spatial dimension. We demonstrate that this, nontrivially, remains true also for long-range interactions in two spatial dimensions. We, finally, find that fragmentation in a single well is a mesoscopic phenomenon: Within our fully self-consistent approach, the degree of fragmentation, to a good approximation, decreases universally as N-1 /2 when only N is varied.
Uwe R. Fischer; Axel U. J. Lode; Budhaditya Chatterjee
2015-02-17
The occupation of more than one single-particle state and hence the emergence of fragmentation is a many-body phenomenon universal to systems of spatially confined interacting bosons. In the present study, we investigate the effect of the range of the interparticle interactions on the fragmentation degree of one- and two-dimensional systems. We solve the full many-body Schr\\"odinger equation of the system using the recursive implementation of the multiconfigurational time-dependent Hartree for bosons method, R-MCTDHB. The dependence of the degree of fragmentation on dimensionality, particle number, areal or line density and interaction strength is assessed. It is found that for contact interactions, the fragmentation is essentially density independent in two dimensions. However, fragmentation increasingly depends on density the more long-ranged the interactions become. The degree of fragmentation is increasing, keeping the particle number $N$ fixed, when the density is decreasing as expected in one spatial dimension. We demonstrate that this remains, nontrivially, true also for long-range interactions in two spatial dimensions. We, finally, find that within our fully self-consistent approach, the fragmentation degree, to a good approximation, decreases universally as $N^{-1/2}$ when only $N$ is varied.
Understanding the many-body expansion for large systems. I. Precision considerations
NASA Astrophysics Data System (ADS)
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2014-07-01
Electronic structure methods based on low-order "n-body" expansions are an increasingly popular means to defeat the highly nonlinear scaling of ab initio quantum chemistry calculations, taking advantage of the inherently distributable nature of the numerous subsystem calculations. Here, we examine how the finite precision of these subsystem calculations manifests in applications to large systems, in this case, a sequence of water clusters ranging in size up to (H_2O)_{47}. Using two different computer implementations of the n-body expansion, one fully integrated into a quantum chemistry program and the other written as a separate driver routine for the same program, we examine the reproducibility of total binding energies as a function of cluster size. The combinatorial nature of the n-body expansion amplifies subtle differences between the two implementations, especially for n ? 4, leading to total energies that differ by as much as several kcal/mol between two implementations of what is ostensibly the same method. This behavior can be understood based on a propagation-of-errors analysis applied to a closed-form expression for the n-body expansion, which is derived here for the first time. Discrepancies between the two implementations arise primarily from the Coulomb self-energy correction that is required when electrostatic embedding charges are implemented by means of an external driver program. For reliable results in large systems, our analysis suggests that script- or driver-based implementations should read binary output files from an electronic structure program, in full double precision, or better yet be fully integrated in a way that avoids the need to compute the aforementioned self-energy. Moreover, four-body and higher-order expansions may be too sensitive to numerical thresholds to be of practical use in large systems.
Understanding the many-body expansion for large systems. I. Precision considerations
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2014-07-07
Electronic structure methods based on low-order “n-body” expansions are an increasingly popular means to defeat the highly nonlinear scaling of ab initio quantum chemistry calculations, taking advantage of the inherently distributable nature of the numerous subsystem calculations. Here, we examine how the finite precision of these subsystem calculations manifests in applications to large systems, in this case, a sequence of water clusters ranging in size up to (H{sub 2}O){sub 47}. Using two different computer implementations of the n-body expansion, one fully integrated into a quantum chemistry program and the other written as a separate driver routine for the same program, we examine the reproducibility of total binding energies as a function of cluster size. The combinatorial nature of the n-body expansion amplifies subtle differences between the two implementations, especially for n ? 4, leading to total energies that differ by as much as several kcal/mol between two implementations of what is ostensibly the same method. This behavior can be understood based on a propagation-of-errors analysis applied to a closed-form expression for the n-body expansion, which is derived here for the first time. Discrepancies between the two implementations arise primarily from the Coulomb self-energy correction that is required when electrostatic embedding charges are implemented by means of an external driver program. For reliable results in large systems, our analysis suggests that script- or driver-based implementations should read binary output files from an electronic structure program, in full double precision, or better yet be fully integrated in a way that avoids the need to compute the aforementioned self-energy. Moreover, four-body and higher-order expansions may be too sensitive to numerical thresholds to be of practical use in large systems.
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2004-12-01
We take advantage of the simple approach, recently discussed, which associates to (solvable) matrix equations (solvable) dynamical systems interpretable as (interesting) many-body problems, possibly involving auxiliary dependent variables in addition to those identifying the positions of the moving particles. Starting from a solvable matrix evolution equation, we obtain the corresponding many-body model and note that in one case the auxiliary variables can be altogether eliminated, obtaining thereby an (also Hamiltonian) extension of the "goldfish" model. The solvability of this novel model, and of its isochronous variant, is exhibited. A related, as well solvable, model, is also introduced, as well as its isochronous variant. Finally, the small oscillations of the isochronous models around their equilibrium configurations are investigated, and from their isochronicity certain diophantine relations are evinced.
Atomic Many-Body Theory Applied to Photoionization Processes in Complex Open-Shell Systems.
NASA Astrophysics Data System (ADS)
Boyle, James John
In this work, we examine the process of photoionization of complex open-shell atoms within the context of many -body perturbation theory (MBPT). A single-particle potential for excited states is introduced which is based on a potential defined by Qian et al.^{[ 1] } Analytic properties of this potential are derived using graphical techniques of angular momentum coupling. Values of the potential are tabulated for all s^{n}, p^{n }, and d^{n} initial state couplings. We have performed a photoionization cross section calculation of atomic tungsten for photon energies from threshold to 150 eV using the generalized resonance technique ^{[ 2]} over several LSJ couplings of the initial state. Although the formalism behind the generalized resonance technique has been discussed previously (ref. 2 of abstract), this work represents the first explicit use of this technique. Non -relativistic orbitals are used in the basis set, and relativistic corrections have been included. We consider excitations from the 4f, 5s, 5p, 5d, and 6s subshells. The effect of the strong 5p^{6}5d^{4} to 5p^{5}5d^5 and 4f^{14}5d^4to 4f ^{13}5d^5 transitions are included as resonant contributions to the 5d partial cross section. Specifically, we consider three LSJ couplings of the 5d subshell in the initial state. For the first case we consider the initial state to be 5d^4[^{5 }D_{J=0}]. In the second we place more emphasis on the J value by diagonalizing the initial state with respect to the spin-orbit Hamiltonian and the eigenstates 5d^4[^ {5}D, _sp{2}{3}P, _sp{4}{3}P, _sp {0}{1}S, _sp{4} {1}S] all coupled to J=0 . Thirdly, we remove the dependence of the initial state upon the J value by computing the cross sections for 5d^4[^{5}D _{j=0,1,2,3,4}], summing the results and weighting by (2J+1). Our results indicate that the 5d partial cross section dominates the total cross section below 100 eV. References. 1. Z. Qian, S. L. Carter, and H. P. Kelly, Phys. Rev. A, 33, 1751 (1986). 2. L. J. Garvin, A Study of Photoionization, including Resonance Structure and Spin-Orbit effects, in Atomic Manganese, Ph.D. Thesis, Univ. of Virginia (unpublished) (1983) pp. 128-45.
Lathrop, Daniel P.
Physics 832: Quantum Many-Body Physics Fall 2011 Lecture: TuTh 2:003:15 in Phy 2202 by Michael Levin (Office: Phy 2220). Prerequisites: Quantum mechanics (Physics 402), Statistical physics (Physics 404). Philosophy: This course will introduce some of the basic tools and physical pictures nec- essary
Principle of Maximum Entanglement Entropy and Local Physics of Correlated many-body Electron-Systems
NASA Astrophysics Data System (ADS)
Lanata, Nicola; Strand, Hugo; Yao, Yongxin; Kotliar, Gabriel
2014-03-01
We argue that, because of the quantum-entanglement, the local physics of the strongly-correlated materials at zero temperature is described in very good approximation by a simple generalized Gibbs distribution, which depends on a relatively small number local quantum thermodynamical potentials. We demonstrate that our statement is exact in certain limits, and we perform numerical calculations of the iron compounds FeSe and FeTe and of the elemental cerium by employing the Gutzwiller Approximation (GA) that strongly support our theory in general.
Advancing Large Scale Many-Body QMC Simulations on GPU accelerated Multicore Systems
California at Davis, University of
, the combination of multi-socket multi-core processors and GPUs provide widely available platforms of the magnetic and transport properties of layered materials with DQMC. Keywords-Quantum Monte Carlo; QRP correlations and metal-insulator transitions of this Hamil- tonian [5], [6], [7], [8], [9], [10], [11], [12
Bold-line Monte Carlo and the nonequilibrium physics of strongly correlated many-body systems
NASA Astrophysics Data System (ADS)
Cohen, Guy
2015-03-01
This talk summarizes real time bold-line diagrammatic Monte-Carlo approaches to quantum impurity models, which make significant headway against the sign problem by summing over corrections to self-consistent diagrammatic expansions rather than a bare diagrammatic series. When the bold-line method is combined with reduced dynamics techniques both local single-time properties and two time correlators such as Green functions can be computed at very long timescales, enabling studies of nonequilibrium steady state behavior of quantum impurity models and creating new solvers for nonequilibrium dynamical mean field theory. This work is supported by NSF DMR 1006282, NSF CHE-1213247, DOE ER 46932, TG-DMR120085 and TG-DMR130036, and the Yad Hanadiv-Rothschild Foundation.
Introduction to the Statistical Physics of Integrable Many-body Systems
NASA Astrophysics Data System (ADS)
Šamaj, Ladislav Å.; Bajnok, Zoltán
2013-05-01
Preface; Part I. Spinless Bose and Fermi Gases: 1. Particles with nearest-neighbour interactions: Bethe ansatz and the ground state; 2. Bethe ansatz: zero-temperature thermodynamics and excitations; 3. Bethe ansatz: finite-temperature thermodynamics; 4. Particles with inverse-square interactions; Part II. Quantum Inverse Scattering Method: 5. QISM: Yang-Baxter equation; 6. QISM: transfer matrix and its diagonalization; 7. QISM: treatment of boundary conditions; 8. Nested Bethe ansatz for spin-1/2 fermions with delta interactions; 9. Thermodynamics of spin-1/2 fermions with delta interactions; Part III. Quantum Spin Chains: 10. Quantum Ising chain in a transverse field; 11. XXZ Heisenberg chain: Bethe ansatz and the ground state; 12. XXZ Heisenberg chain: ground state in the presence of magnetic field; 13. XXZ Heisenberg chain: excited states; 14. XXX Heisenberg chain: thermodynamics with strings; 15. XXZ Heisenberg chain: thermodynamics without strings; 16. XYZ Heisenberg chain; 17. Integrable isotropic chains with arbitrary spin; Part IV. Strongly Correlated Electrons: 18. Hubbard model; 19. Kondo effect; 20. Luttinger many-fermion model; 21. Integrable BCS superconductors; Part V. Sine-Gordon Model: 22. Classical sine-Gordon theory; 23. Conformal quantization; 24. Lagrangian quantization; 25. Bootstrap quantization; 26. UV-IR relation; 27. Exact finite volume description from XXZ; 28. Two-dimensional Coulomb gas; Appendix A. Spin and spin operators on chain; Appendix B. Elliptic functions; References; Index.
(The physics of cellular automata and coherence and chaos in classical many-body systems)
Not Available
1992-06-24
This report contains short discussions on the following topics: non-variational effects in a Ginzburg-Landau equation; algebraic correlations in conserved chaotic systems; chaotic interface models of turbulence; algebraic correlations in coupled order parameter systems; and dynamics of Josephson Junction arrays. (LSP)
NASA Astrophysics Data System (ADS)
Damanik, David; Lukic, Milivoje; Yessen, William
2015-08-01
We investigate quantum dynamics with the underlying Hamiltonian being a Jacobi or a block Jacobi matrix with the diagonal and the off-diagonal terms modulated by a periodic or a limit-periodic sequence. In particular, we investigate the transport exponents. In the periodic case we demonstrate ballistic transport, while in the limit-periodic case we discuss various phenomena, such as quasi-ballistic transport and weak dynamical localization. We also present applications to some quantum many body problems. In particular, we establish for the anisotropic XY chain on with periodic parameters an explicit strictly positive lower bound for the Lieb-Robinson velocity.
Multi-meson systems in lattice QCD / Many-body QCD
Detmold, William [College of William and Mary, Williamsburg, VA (United States)
2013-08-31
Nuclear physics entails the study of the properties and interactions of hadrons, such as the proton and neutron, and atomic nuclei and it is central to our understanding of our world at the smallest scales. The underlying basis for nuclear physics is provided by the Standard Model of particle physics which describes how matter interacts through the strong, electromagnetic and weak (electroweak) forces. This theory was developed in the 1970s and provides an extremely successful description of our world at the most fundamental level to which it has been probed. The Standard Model has been, and continues to be, subject to stringent tests at particle accelerators around the world, so far passing without blemish. However, at the relatively low energies that are relevant for nuclear physics, calculations involving the strong interaction, governed by the equations of Quantum Chromodynamics (QCD), are enormously challenging, and to date, the only systematic way to perform them is numerically, using a framework known as lattice QCD (LQCD). In this approach, one discretizes space-time and numerically solves the equations of QCD on a space-time lattice; for realistic calculations, this requires highly optimized algorithms and cutting-edge high performance computing (HPC) resources. Progress over the project period is discussed in detail in the following subsections
Heat Engine Driven by Photon Tunneling in Many-Body Systems
NASA Astrophysics Data System (ADS)
Latella, Ivan; Pérez-Madrid, Agustín; Rubi, J. Miguel; Biehs, Svend-Age; Ben-Abdallah, Philippe
2015-07-01
Near-field heat engines are devices that convert the evanescent thermal field supported by a primary source into usable mechanical energy. By analyzing the thermodynamic performance of three-body near-field heat engines, we demonstrate that the power they supply can be substantially larger than that of two-body systems, showing their strong potential for energy harvesting. Theoretical limits for energy and entropy fluxes in three-body systems are discussed and compared with their corresponding two-body counterparts. Such considerations confirm that the thermodynamic availability in energy-conversion processes driven by three-body photon tunneling can exceed the thermodynamic availability in two-body systems.
Double decimation and sliding vacua in the nuclear many-body system
NASA Astrophysics Data System (ADS)
Brown, G. E.; Rho, Mannque
2004-06-01
We propose that effective field theories for nuclei and nuclear matter comprise of “double decimation”: (1) the chiral symmetry decimation (CSD) and (2) Fermi liquid decimation (FLD). The Brown-Rho scaling recently identified as the parametric dependence intrinsic in the “vector manifestation” of hidden local symmetry theory of Harada and Yamawaki results from the first decimation. This scaling governs dynamics down to the scale at which the Fermi surface is formed as a quantum critical phenomenon. The next decimation to the top of the Fermi sea where standard nuclear physics is operative makes up the FLD. Thus, nuclear dynamics are dictated by two fixed points, namely, the vector manifestation fixed point and the Fermi liquid fixed point. It has been a prevalent practice in nuclear physics community to proceed with the second decimation only, assuming density-independent masses, without implementing the first, CSD. We show why most nuclear phenomena can be reproduced by theories using either density-independent, or density-dependent masses, a grand conspiracy of nature that is an aspect that could be tied to the Cheshire Cat phenomenon in hadron physics. We identify what is left out in the FLD that does not incorporate the CSD. Experiments such as the dilepton production in relativistic heavy ion reactions, which are specifically designed to observe effects of dropping masses, could exhibit large effects from the reduced masses. However, they are compounded with effects that are not directly tied to chiral symmetry. We discuss a recent STAR/RHIC observation where BR scaling can be singled out in a pristine environment.
Y. M. Zhao; A. Arima; N. Yoshinaga
2002-06-18
In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.
a Solvable Model of Interacting Many Body Systems Exhibiting a Breakdown of the Boltzmann Equation
NASA Astrophysics Data System (ADS)
McKellar, B. H. J.
2014-12-01
In a particular exactly solvable model of an interacting system, the Boltzmann equation predicts a constant single particle density operator, whereas the exact solution gives a single particle density operator with a nontrivial time dependence. All of the time dependence of the single particle density operator is generated by the correlations.
Raizen, Mark G.
Quantum Many-Body Culling: Production of a Definite Number of Ground-State Atoms in a Bose a definite number of ground-state atoms by adiabatic reduction of the depth of a potential well that confines scales for adiabaticity and discuss the recent observation of atomic number squeezing [Chuu et al., Phys
Anomalous decoherence and absence of thermalization in a photonic many-body system
Larson, Jonas [Department of Physics, Stockholm University, AlbaNova University Center, SE-10691 Stockholm (Sweden)
2011-05-15
The intention of this work is twofold: first, to present a most simple system capable of simulating the intrinsic bosonic Josephson effect with photons and, second, to study various outcomes deriving from inherent or external decoherence. A qubit induces an effective coupling between two externally pumped cavity modes. Without cavity losses and in the dispersive regime, intrinsic Josephson oscillations of photons between the two modes occurs. In this case, contrary to regular Markovian decoherence, the qubit purity shows a Gaussian decay and recurrence of its coherence. Due to intrinsic nonlinearities, both the Josephson oscillations as well as the qubit properties display a rich collapse-revival structure, where, however, the complexity of the qubit evolution is in some sense stronger. The qubit as a meter of the photon dynamics is considered, and it is shown that qubit dephasing, originating, for example, from nondemolition measurements, results in an exponential destruction of the oscillations which manifests the collectiveness of the Josephson effect. Nonselective qubit measurements, on the other hand, render a Zeno effect seen in a slowing down of the Josephson oscillations. Contrary to dephasing, cavity dissipation results in a Gaussian decay of the scaled Josephson oscillations. Finally, following Ponomarev et al. [Phys. Rev. Lett. 106, 010405 (2011)], we analyze aspects of thermalization. In particular, despite similarities with the generic model studied by Ponomarev et al., our system does not seem to thermalize.
Many-body effects on optical gain in GaAsPN/GaPN quantum well lasers for silicon integration
Park, Seoung-Hwan
2014-02-14
Many-body effects on the optical gain in GaAsPN/GaP QW structures were investigated by using the multiband effective-mass theory and the non-Markovian gain model with many-body effects. The free-carrier model shows that the optical gain peak slightly increases with increasing N composition. In addition, the QW structure with a larger As composition shows a larger optical gain than that with a smaller As composition. On the other hand, in the case of the many-body model, the optical gain peak decreases with increasing N composition. Also, the QW structure with a smaller As composition is observed to have a larger optical gain than that with a larger As composition. This can be explained by the fact that the QW structure with a smaller As or N composition shows a larger Coulomb enhancement effect than that with a larger As or N composition. This means that it is important to consider the many-body effect in obtaining guidelines for device design issues.
Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems
Schönleber, David W; Evers, Jörg
2014-01-01
We study the impact of dephasing on the excitation dynamics of a cloud of ultracold two-level Rydberg atoms for both resonant and off-resonant laser excitation, using the wave function Monte Carlo (MCWF) technique. We find that while for resonant laser driving, dephasing mainly leads to an increase of the Rydberg population and a decrease of the Mandel Q parameter, at off-resonant driving strong dephasing toggles between direct excitation of pairs of atoms and subsequent excitation of single atoms, respectively. These two excitation mechanisms can be directly quantified via the pair correlation function, which shows strong suppression of the two-photon resonance peak for strong dephasing. Consequently, qualitatively different dynamics arise in the excitation statistics for weak and strong dephasing in off-resonant excitation. Our findings show that time-resolved excitation number measurements can serve as a powerful tool to identify the dominating process in the system's excitation dynamics.
Coherent versus incoherent excitation dynamics in dissipative many-body Rydberg systems
David W. Schönleber; Martin Gärttner; Jörg Evers
2014-01-28
We study the impact of dephasing on the excitation dynamics of a cloud of ultracold two-level Rydberg atoms for both resonant and off-resonant laser excitation, using the wave function Monte Carlo (MCWF) technique. We find that while for resonant laser driving, dephasing mainly leads to an increase of the Rydberg population and a decrease of the Mandel Q parameter, at off-resonant driving strong dephasing toggles between direct excitation of pairs of atoms and subsequent excitation of single atoms, respectively. These two excitation mechanisms can be directly quantified via the pair correlation function, which shows strong suppression of the two-photon resonance peak for strong dephasing. Consequently, qualitatively different dynamics arise in the excitation statistics for weak and strong dephasing in off-resonant excitation. Our findings show that time-resolved excitation number measurements can serve as a powerful tool to identify the dominating process in the system's excitation dynamics.
Parametrization of a reactive many-body potential for Mo-S systems
NASA Astrophysics Data System (ADS)
Liang, Tao; Phillpot, Simon R.; Sinnott, Susan B.
2009-06-01
We present an interatomic potential for the Mo-S system based on the second-generation reactive empirical bond-order formalism. An analytic function is introduced to the bond-order term to capture the effect of the coordination number on the binding energy. The fitting scheme used for this potential is optimized by appropriate selection of the functions, training databases, initial guesses, and weights on each residual—the four factors that are involved in a weighted nonlinear least-squares fitting. The resulting potential is able to yield good agreement with the structure and energetics of Mo molecules, two-dimensional Mo structures, three-dimensional Mo crystals, small S molecules, and binary Mo-S crystal structures. We illustrate the capabilities of the new potential by presenting results of the simulation of friction between MoS2 layers. The results are consistent with our previous static potential surface calculations using density-functional theory.
Formalism for Matrix Elements of Many-Body Systems from Dimensional Perturbation Theory
NASA Astrophysics Data System (ADS)
Dunn, Martin; McKinney, Brett; Watson, Deborah
2002-05-01
Dimensional Perturbation Theory (DPT) for atomic and molecular systems involves a perturbation expansion in powers of 1/D about the exactly-soluble, zeroth-order, infinite-dimensional solution. A key element in the development of DPT is a similarity transform of the operators and wave function under which the kinetic energy term is transformed to two terms. The first term involves derivatives while the second has the form of a potential energy. When the transforming function is chosen to involve the Grammian determinant, only the second term remains as D and so the problem becomes a static potential problem. In large dimensions, oscillations about this infinite-dimensional structure are simple harmonic normal modes which allows for physical insight and greatly simplifies the calculation of higher-order terms. This formalism works well when it comes to calculating energies, but matrix elements are a problem since the integrals involve a weight function that is difficult to calculate. We present a formalism which introduces a further similarity transform under which the weight function becomes unity while preserving the crucial features of the Grammian determinant transformation. Since the weight function is unity, the physical interpretation of the large-dimension normal mode structure also becomes more transparent as the post transformation derivatives are now the conjugate momenta to the coordinate variables.
Multiple-time-scale Landau-Zener transitions in many-body systems
NASA Astrophysics Data System (ADS)
Larson, Jonas
2015-01-01
Motivated by recent cold-atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunneling between neighboring lattice sites this on-site single-particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single-site Landau-Zener transitions, also implies, in the presence of a confining trap, an intersite particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and intersite dynamics. The adiabaticity constraint is therefore not simply given by the standard one, the Hamiltonian rate of change relative to the gap of the on-site problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics; e.g., nonadiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close-to-perfect on-site transitions take place.
The Loschmidt Echo as a robust decoherence quantifier for many-body systems
Pablo R. Zangara; Axel D. Dente; Patricia R. Levstein; Horacio M. Pastawski
2012-07-23
We employ the Loschmidt Echo, i.e. the signal recovered after the reversal of an evolution, to identify and quantify the processes contributing to decoherence. This procedure, which has been extensively used in single particle physics, is here employed in a spin ladder. The isolated chains have 1/2 spins with XY interaction and their excitations would sustain a one-body like propagation. One of them constitutes the controlled system S whose reversible dynamics is degraded by the weak coupling with the uncontrolled second chain, i.e. the environment E. The perturbative SE coupling is swept through arbitrary combinations of XY and Ising like interactions, that contain the standard Heisenberg and dipolar ones. Different time regimes are identified for the Loschmidt Echo dynamics in this perturbative configuration. In particular, the exponential decay scales as a Fermi golden rule, where the contributions of the different SE terms are individually evaluated and analyzed. Comparisons with previous analytical and numerical evaluations of decoherence based on the attenuation of specific interferences, show that the Loschmidt Echo is an advantageous decoherence quantifier at any time, regardless of the S internal dynamics.
Strong and weak chaos in weakly nonintegrable many-body Hamiltonian systems
Mario Mulansky; Karsten Ahnert; Arkady Pikovsky; Dima Shepelyansky
2011-03-15
We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators, by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the measure of chaos is found to be proportional to the coupling strength and lattice length, with the typical maximal Lyapunov exponent being proportional to the square root of coupling. This strong chaos appears as a result of triplet resonances between nearby modes. In addition to strong chaos we observe a weakly chaotic component having much smaller Lyapunov exponent, the measure of which drops approximately as a square of the coupling strength down to smallest couplings we were able to reach. We argue that this weak chaos is linked to the regime of fast Arnold diffusion discussed by Chirikov and Vecheslavov. In disordered lattices of large size we find a subdiffusive spreading of initially localized wave packets over larger and larger number of modes. The relations between the exponent of this spreading and the exponent in the dependence of the fast Arnold diffusion on coupling strength are analyzed. We also trace parallels between the slow spreading of chaos and deterministic rheology.
Multiple-time-scale Landau-Zener transitions in many-body systems
Jonas Larson
2015-01-27
Motivated by recent cold atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunnelling between neighboring lattice sites this onsite single particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single site Landau-Zener transitions, also implies, in the presence of a confining trap, an inter-site particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and inter-site dynamics. The adiabaticity constrain is therefor not simply given by the standard one; the Hamiltonian rate of change relative to the gap of the onsite problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics, e.g. non-adiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close to perfect onsite transitions take place.
NASA Astrophysics Data System (ADS)
Sanders, Lloyd P.; Lomholt, Michael A.; Lizana, Ludvig; Fogelmark, Karl; Metzler, Ralf; Ambjörnsson, Tobias
2014-11-01
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form < {{x}2}(t)> ? {{t}? } of the mean squared displacement with 0\\lt ? \\lt 1, we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics < {{x}2}(t)> ? {{log }1/2}t with a universal 1/2 exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement < {{x}2}(t)> ? {{t}? } with 0\\lt ? \\lt 1/2, that is slower than the famed Harris law < {{x}2}(t)> ? {{t}1/2} without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.
Relativistic nuclear many-body theory
Serot, B.D. ); Walecka, J.D. . Continuous Electron Beam Accelerator Facility)
1991-09-11
Nonrelativistic models of nuclear systems have provided important insight into nuclear physics. In future experiments, nuclear systems will be examined under extreme conditions of density and temperature, and their response will be probed at momentum and energy transfers larger than the nucleon mass. It is therefore essential to develop reliable models that go beyond the traditional nonrelativistic many-body framework. General properties of physics, such as quantum mechanics, Lorentz covariance, and microscopic causality, motivate the use of quantum field theories to describe the interacting, relativistic, nuclear many-body system. Renormalizable models based on hadronic degrees of freedom (quantum hadrodynamics) are presented, and the assumptions underlying this framework are discussed. Some applications and successes of quantum hadrodynamics are described, with an emphasis on the new features arising from relativity. Examples include the nuclear equation of state, the shell model, nucleon-nucleus scattering, and the inclusion of zero-point vacuum corrections. Current issues and problems are also considered, such as the construction of improved approximations, the full role of the quantum vacuum, and the relationship between quantum hadrodynamics and quantum chromodynamics. We also speculate on future developments. 103 refs., 18 figs.
Self-similar non-equilibrium dynamics of a many-body system with power-law interactions
Gutiérrez, Ricardo; Lesanovsky, Igor
2015-01-01
The influence of power-law interactions on the dynamics of many-body systems far from equilibrium is much less explored than their effect on static and thermodynamic properties. To gain insight into this problem we introduce and analyze here an out-of-equilibrium deposition process in which the deposition rate of a given particle depends as a power-law on the distance to previously deposited particles. Although rather simplistic this model draws its relevance from recent experimental progress in the domain of cold atomic gases which are studied in a setting where atoms that are excited to high-lying Rydberg states interact through power-law potentials that translate into power-law excitation rates. The out-of-equilibrium dynamics of this system turns out to be surprisingly rich. It features a self-similar evolution which leads to a characteristic power-law time dependence of observables such as the particle concentration and results in a scale invariance of the structure factor. Moreover, it displays a crosso...
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2015-09-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ?slant n ?slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
NASA Astrophysics Data System (ADS)
Dougherty, Randy Wade
The Relativistic Linked-Cluster Many-Body Perturbation Theory (RLCMBPT) technique has been successfully applied to the study of the magnetic dipole hyperfine interaction in a variety of atomic and ionic systems. The RLCMBPT procedure has produced theoretical results which agree well with those experimental results which are available. In addition, the RLCMBPT method makes it possible to calculate the contributions to the hyperfine field at the nucleus created by specific physical mechanisms whose contributions to the total field cannot be found by experiment. Specifically, the contributions coming from core polarization and correlation effects, as well as the direct contribution from the (unperturbed) valence electron are calculated for each system. Comparing the contributions from these separate mechanisms in related systems gives valuable insights into the physical behavior of these systems; such comparisons are made whenever possible. Comparisons are also made, when possible, to the results of previous calculations of these properties made by others using differing techniques. Such comparisons help to evaluate the efficacy of all the methods being compared. The first set of systems studied are the three -electron ions (with 1s^2 2s electronic configuration) of the atoms in the second row of the periodic table, Li^0, Be^+ , B^{+2} C ^{+3}, N^{+4 }, O^{+5}, F^{+6}, Ne^ {+7}, as well as the Bi^ {+80} ion, which is studied as an extreme case. These systems are the simplest many-electron ions which have non-vanishing hyperfine interactions. An estimate of the contribution to the hyperfine field coming from radiative corrections is made, in order to discover the relative importance of radiative effects so that the possibility of experimentally measuring the radiative contribution can be estimated. A similar study (excluding the radiative effect estimate) is made on several states of the Ra^+ ion. In addition to the ground state (7s) of the system, the excited 7p_{1over2 } state is investigated, along with the 8s -12s excited s states. Finally, the results of a calculation of the hyperfine interaction in the Cu, Ag and Au atoms are presented. The great importance of correlation within the outermost d shells in these systems is discussed.
Few- and many-body physics of dipoles in ion traps and optical lattice simulators
Safavi-Naini, Arghavan
2014-01-01
The presence of strong interactions in quantum many-body systems makes the analytical treatment of such systems very difficult. In this thesis we explore two possible proposals for simulating strongly correlated, quantum ...
Garrahan, Juan P.
and Astronomy, The University of Nottingham, Nottingham, NG7 2RD, United Kingdom 2 Midlands Ultracold Atom Research Centre (MUARC), The University of Nottingham, Nottingham, NG7 2RD, United Kingdom (Received 5- malization.'' The study of closed quantum systems and their relaxation behavior has recently received renewed
Boal, David
PHYS415 Lecture 10 - Many-body systems: non-interacting 1 Â© 1996 by David Boal, Simon Fraser - Many-body systems: non-interacting 2 Â© 1996 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. #12;PHYS415 Lecture 10 - Many-body systems: non
Georgescu, Ionu? Mandelshtam, Vladimir A.; Jitomirskaya, Svetlana
2013-11-28
Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCP approximation.
Turner, Daniel B.
Studies have shown that many-body interactions among semiconductor excitons can produce distinct features in two-dimensional optical spectra. However, to the best of our knowledge, the dynamics of many-body interactions ...
Diehl, S.; Daley, A. J.; Zoller, P. [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Baranov, M. [Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); RRC 'Kurchatov Institute', Kurchatov Square 1, 123182 Moscow (Russian Federation)
2010-08-01
We analyze the ground-state phase diagram of attractive lattice bosons, which are stabilized by a three-body onsite hardcore constraint. A salient feature of this model is an Ising-type transition from a conventional atomic superfluid to a dimer superfluid with vanishing atomic condensate. The study builds on an exact mapping of the constrained model to a theory of coupled bosons with polynomial interactions, proposed in a related paper [S. Diehl, M. Baranov, A. Daley, and P. Zoller, Phys. Rev. B 82, 064509 (2010).]. In this framework, we focus by analytical means on aspects of the phase diagram which are intimately connected to interactions, and are thus not accessible in a mean-field plus spin-wave approach. First, we determine shifts in the mean-field phase border, which are most pronounced in the low-density regime. Second, the investigation of the strong coupling limit reveals the existence of a 'continuous supersolid', which emerges as a consequence of enhanced symmetries in this regime. We discuss its experimental signatures. Third, we show that the Ising-type phase transition, driven first order via the competition of long-wavelength modes at generic fillings, terminates into a true Ising quantum critical point in the vicinity of half filling.
D. Bohm; G. Carmi
1964-01-01
In two papers (of which this is the first) our central concern is to draw conclusions about the over-all dynamical properties of a many-body system. This is done without trying to solve the equations of motion, but rather, on the basis of our knowledge of oscillatory or collective variables (or more generally, from the existence of conservation rules and of
Cui, H. T.
2010-04-15
Overlap with the separable state is introduced in this article for the purpose of characterizing the overall correlation in many-body systems. This definition has clear geometric and physical meaning and moreover can be considered as the generalization of the concept of the Anderson orthogonality catastrophe. As an exemplification, it is used to mark the phase transition in the Dicke model for zero and finite temperatures, and the discussion shows that it can faithfully reflect the phase transition properties of this model whether for zero or finite temperature. Furthermore, the overlap for the ground state also indicates the appearance of multipartite entanglement in the Dicke model.
NASA Astrophysics Data System (ADS)
Kim, Yeong E.; Koltick, David S.; Zubarev, Alexander L.
2005-12-01
There have been a number of reports of observation of nuclear fusion events in acoustic cavitation experiments with deuterated liquid. Some of the reported results have been interpreted as a result of achieving thermonuclear fusion temperatures (~a few keV) during acoustic bubble cavitation (ABC). We propose an alternative theoretical model for the ABC fusion based on Bose-Einstein condensation (BEC) mechanism. Our theoretical model yields two main predictions. The first prediction is that the Coulomb interaction between two charged bosons is suppressed for the case in which number N of charged bosons is large, and hence the conventional Gamow factor is absent. The second prediction is that the fusion rate depends on the probability of the BEC ground state occupation instead of the conventional Gamow factor. This implies that the fusion rate will increase as the temperature of the system is lowered since the probability of the BEC state is larger at lower temperatures. These predictions imply that the ABC fusion may be achievable at lower temperatures. A number of key improvement to acoustic cavitation experiments are proposed to check these predictions as well as the results of other experiments.
Many-Body Physics, Topology and Geometry
NASA Astrophysics Data System (ADS)
Sen, Siddhartha; Gupta, Kumar Sankar
2015-06-01
The challenge of condensed matter physics is to use non relativistic quantum ideas to explain and predict the observed oscopic properties of matter. To do this great ingenuity and imagination is required. The Hamiltonian H of a many-body system can be written down schematically as
Many-body entanglement: Permutations and equivalence classes
Florian Mintert; Benno Salwey; Andreas Buchleitner
2012-09-26
With an easily applicable criterion based on permutation symmetries of (identically prepared) replicas of quantum states we identify distinct entanglement classes in high-dimensional multi- partite systems. The different symmetry properties of inequivalent states provide a rather intuitive picture of the otherwise very abstract classification of many-body entangled states.
Nuclear Many-Body Physics Where Structure And Reactions Meet
Naureen Ahsan; Alexander Volya
2009-06-24
The path from understanding a simple reaction problem of scattering or tunneling to contemplating the quantum nuclear many-body system, where structure and continuum of reaction-states meet, overlap and coexist, is a complex and nontrivial one. In this presentation we discuss some of the intriguing aspects of this route.
NASA Astrophysics Data System (ADS)
MacDonald, Allan H.
2014-03-01
Most current electronic devices use gate voltages to switch individual electron transport channels or off. This architecture necessarily leads to operating voltages that are much larger than the temperature thermal energy, and places lower bounds on power consumption that are becoming. I will discuss strategies for achieving devices in which gates are used to collective many-electron states, in principle allowing charge transport to be switched by smaller voltage changes and both operating voltages and power consumption to reduced. I will specifically address devices based on the properties of itinerant electroninsulating magnetic systems, and devices based on bilayer exciton condensation. This work is based on work performed in collaboration with Sanjay Banerjee and Frank Register.
Interferometric Probes of Many-Body Localization
Knap, M.
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set ...
Scalable dissipative preparation of many-body entanglement
Florentin Reiter; David Reeb; Anders S. Sørensen
2015-01-26
Entanglement is an essential resource for quantum information, quantum computation and quantum communication. While small entangled states of few particles have been used to demonstrate non-locality of nature and elementary quantum communication protocols, more advanced quantum computation and simulation tasks as well as quantum-enhanced measurements require many-body entanglement. Over the past years, impressive progress has been made on entangling larger numbers of qubits using unitary quantum gates. Entangled states are, however, sensitive to interactions with the environment, which are present in any open system. In particular decoherence and dissipation have remained a challenge. Here we show that by taking an approach alternative to quantum gates one can actively use dissipation to generate many-body entanglement. We demonstrate that by adding sources of dissipation and engineering decay processes, multi-particle entangled states can be prepared efficiently as steady states of the dissipative time evolution. Our protocols pave the way for the dissipative production of many-body entanglement in physical systems such as trapped ions.
Rabani, Eran
We propose a new method to calculate ground state position dependent observables in quantum many American Institute of Physics. S0021-9606 99 51313-5 I. INTRODUCTION Ground state properties of quantum and a birthdeath process is used to propagate a distribution in imaginary time, so that the contribution from
Not Available
1992-06-24
This report contains short discussions on the following topics: non-variational effects in a Ginzburg-Landau equation; algebraic correlations in conserved chaotic systems; chaotic interface models of turbulence; algebraic correlations in coupled order parameter systems; and dynamics of Josephson Junction arrays. (LSP)
Itin, A P; Katsnelson, M I
2015-08-14
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role. PMID:26317726
NASA Astrophysics Data System (ADS)
Itin, A. P.; Katsnelson, M. I.
2015-08-01
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles are derived using an averaging method resembling classical canonical perturbation theory. As is known, a high-frequency force may renormalize hopping coefficients, causing interesting phenomena such as coherent destruction of tunneling and creation of artificial gauge fields. We find explicitly additional corrections to the effective Hamiltonians due to interactions, corresponding to nontrivial processes such as single-particle density-dependent tunneling, correlated pair hoppings, nearest neighbor interactions, etc. Some of these processes arise also in multiband lattice models, and are capable of giving rise to a rich variety of quantum phases. The apparent contradiction with other methods, e.g., Floquet-Magnus expansion, is explained. The results may be useful for designing effective Hamiltonian models in experiments with ultracold atoms, as well as in the field of ultrafast nonequilibrium magnetism. An example of manipulating exchange interaction in a Mott-Hubbard insulator is considered, where our corrections play an essential role.
Luca M. Ghiringhelli; Luigi Delle Site
2007-11-12
In a previous work [L.Delle Site, J.Phys.A 40, 2787 (2007)] the derivation of an analytic expression for the kinetic functional of a many-body electron system has been proposed. Though analytical, the formula is still non local (multidimensional) and thus not ideal for numerical applications. In this work, by treating the test case of a uniform gas of interacting spinless electrons, we propose a computational protocol which combines the previous analytic results with the Monte Carlo (MC) sampling of electronic configurations in space. This, we show, leads to an internally consistent scheme to design well founded local kinetic functionals.
Ledvinka, Tomás; Schäfer, Gerhard; Bicák, Jirí
2008-06-27
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered. PMID:18643648
Tomas Ledvinka; Gerhard Schaefer; Jiri Bicak
2008-07-01
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple closed form as a function of canonical variables describing the bodies only. The field is eliminated by solving inhomogeneous wave equations, applying transverse-traceless projections, and using the Routh functional. By including all special relativistic effects our Hamiltonian extends the results described in classical textbooks of theoretical physics. As an application, the scattering of relativistic objects is considered.
Hernandez-Quiroz, Saul; Benet, Luis [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (UNAM), 62210 Cuernavaca, Morelos, Mexico and Facultad de Ciencias, Universidad Autonoma del Estado de Morelos (UAEM), 62209 Cuernavaca, Morelos (Mexico); Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico (UNAM), 62210 Cuernavaca, Morelos (Mexico)
2010-03-15
We study the nearest-neighbor distributions of the k-body embedded ensembles of random matrices for n bosons distributed over two-degenerate single-particle states. This ensemble, as a function of k, displays a transition from harmonic-oscillator behavior (k=1) to random-matrix-type behavior (k=n). We show that a large and robust quasidegeneracy is present for a wide interval of values of k when the ensemble is time-reversal invariant. These quasidegenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of k and discuss the statistical properties of the splittings of these doublets.
Saúl Hernández-Quiroz; Luis Benet
2010-04-12
We study the nearest-neighbor distributions of the $k$-body embedded ensembles of random matrices for $n$ bosons distributed over two-degenerate single-particle states. This ensemble, as a function of $k$, displays a transition from harmonic oscillator behavior ($k=1$) to random matrix type behavior ($k=n$). We show that a large and robust quasi-degeneracy is present for a wide interval of values of $k$ when the ensemble is time-reversal invariant. These quasi-degenerate levels are Shnirelman doublets which appear due to the integrability and time-reversal invariance of the underlying classical systems. We present results related to the frequency in the spectrum of these degenerate levels in terms of $k$, and discuss the statistical properties of the splittings of these doublets.
$\\bar{D}^{0}D^{0*}$ $(D^{0}\\bar{D}^{0*})$ Systems in QCD-Improved Many Body Potential
M. Imran Jamil; Bilal Masud; Faisal Akram; S. M. Sohail Gilani
2015-06-18
For a system of current interest (composed of charm, anticharm quarks and a pair of light ones), we show trends in phenomenological implications of QCD-based improvements to a simple quark model treatment. We employ resonating group method to render this difficult four-body problem manageable. We use a quadratic confinement so as to be able to improve beyond the Born approximation. We report the position of the pole corresponding to $\\bar{D}^{0}D^{0*}$ molecule for the best fit of a model parameter to the relevant QCD simulations. We point out the interesting possibility that the pole can be shifted to $3872$ MeV by introducing another parameter that changes the strength of the interaction. The revised value of this second parameter can guide future trends in modeling of the exotic meson $X(3872)$. We also report the related variations in the $S$-wave spin average cross sections for $\\bar{D}^{0}D^{0*}\\longrightarrow\\omega J/\\psi$ and $\\bar{D}^{0}D^{0*}\\longrightarrow\\rho J/\\psi$ and show that the pole shows its appearance here as well.
Atomistic simulations of stainless steels: a many-body potential for the Fe-Cr-C system
NASA Astrophysics Data System (ADS)
Henriksson, K. O. E.; Björkas, C.; Nordlund, K.
2013-11-01
Stainless steels found in real-world applications usually have some C content in the base Fe-Cr alloy, resulting in hard and dislocation-pinning carbides—Fe3C (cementite) and Cr23C6—being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe-Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell-Brenner-Tersoff form for the entire Fe-Cr-C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe-Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe-Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe.
Atomistic simulations of stainless steels: a many-body potential for the Fe-Cr-C system.
Henriksson, K O E; Björkas, C; Nordlund, K
2013-11-01
Stainless steels found in real-world applications usually have some C content in the base Fe-Cr alloy, resulting in hard and dislocation-pinning carbides-Fe3C (cementite) and Cr23C6-being present in the finished steel product. The higher complexity of the steel microstructure has implications, for example, for the elastic properties and the evolution of defects such as Frenkel pairs and dislocations. This makes it necessary to re-evaluate the effects of basic radiation phenomena and not simply to rely on results obtained from purely metallic Fe-Cr alloys. In this report, an analytical interatomic potential parameterization in the Abell-Brenner-Tersoff form for the entire Fe-Cr-C system is presented to enable such calculations. The potential reproduces, for example, the lattice parameter(s), formation energies and elastic properties of the principal Fe and Cr carbides (Fe3C, Fe5C2, Fe7C3, Cr3C2, Cr7C3, Cr23C6), the Fe-Cr mixing energy curve, formation energies of simple C point defects in Fe and Cr, and the martensite lattice anisotropy, with fair to excellent agreement with empirical results. Tests of the predictive power of the potential show, for example, that Fe-Cr nanowires and bulk samples become elastically stiffer with increasing Cr and C concentrations. High-concentration nanowires also fracture at shorter relative elongations than wires made of pure Fe. Also, tests with Fe3C inclusions show that these act as obstacles for edge dislocations moving through otherwise pure Fe. PMID:24113334
Renormalization group studies of many-body localization
NASA Astrophysics Data System (ADS)
Altman, Ehud
2015-03-01
Quantum correlations do not usually persist for long in systems at finite energy density and disappear once the system thermalizes. But many-body localization offers an alternative paradigm, whereby quantum matter can evade the usual fate of thermal equilibrium and retain retrievable quantum correlations even at high energies. I will survey a dynamical renormalization group (RG) approach used to characterize the novel dynamics and entanglement structures, which develop in the localized phase in lieu of classical thermalization. Then I will present a theory of the transition between the ergodic and the many-body localized phase based on a novel RG framework. Here eigenstate entanglement entropy emerges as a natural scaling variable; the RG describes a change from area-law to volume law entanglement through an intriguing critical point, where the distribution of entanglement entropy becomes maximally broad. The ergodic phase established near the critical point is a Griffiths phase, which exhibits sub-diffusive energy transport and sub-ballistic entanglement propagation. The anomalous diffusion exponent vanishes continuously at the critical point. Before closing I will discuss recent progress in confronting the emerging theoretical understanding of many-body localization with experimental tests. This research is supported in part by the ERC synergy grant UQUAM.
A 2D Array of 100's of Ions for Quantum Simulation and Many-Body Physics in a Penning Trap
NASA Astrophysics Data System (ADS)
Bohnet, Justin; Sawyer, Brian; Britton, Joseph; Bollinger, John
2015-05-01
Quantum simulations promise to reveal new materials and phenomena for experimental study, but few systems have demonstrated the capability to control ensembles in which quantum effects cannot be directly computed. One possible platform for intractable quantum simulations may be a system of 100's of 9Be+ ions in a Penning trap, where the valence electron spins are coupled with an effective Ising interaction in a 2D geometry. Here we report on results from a new Penning trap designed for 2D quantum simulations. We characterize the ion crystal stability and describe progress towards bench-marking quantum effects of the spin-spin coupling using a spin-squeezing witness. We also report on the successful photodissociation of BeH+ contaminant molecular ions that impede the use of such crystals for quantum simulation. This work lays the foundation for future experiments such as the observation of spin dynamics under the quantum Ising Hamiltonian with a transverse field. Supported by a NIST-NRC Research Associateship.
C. M. Naón; M. C. von Reichenbach; M. L. Trobo
1994-09-15
We extend the path-integral approach to bosonization to the case in which the fermionic interaction is non-local. In particular we obtain a completely bosonized version of a Thirring-like model with currents coupled by general (symmetric) bilocal potentials. The model contains the Tomonaga-Luttinger model as a special case; exploiting this fact we study the basic properties of the 1-d spinless fermionic gas: fermionic correlators, the spectrum of collective modes, etc. Finally we discuss the generalization of our procedure to the non-Abelian case, thus providing a new tool to be used in the study of 1-d many-body systems with spin-flipping interactions.
Random matrices, symmetries, and many-body states
Calvin W. Johnson
2011-03-21
All nuclei with even numbers of protons and of neutrons have ground states with zero angular momentum. This is ascribed to the pairing force between nucleons, but simulations with random interactions suggest a much broader many-body phenomenon. In this Letter I project out random Hermitian matrices that have good quantum numbers and, computing the width of the Hamiltonian in subspaces, find ground states dominated by low quantum numbers, e.g. J=0. Furthermore I find odd-$Z$, odd-$N$ systems with isospin conservation have relatively fewer J=0 ground states.
NASA Astrophysics Data System (ADS)
Boyle, J. J.; Pindzola, M. S.
2005-11-01
Preface; Contributors; Introduction; Part I. Atomic Structure: 1. Development of atomic many-body theory Ingvar Lindgren; 2. Relativistic MBPT for highly charged ions W. R. Johnson; 3. Parity nonconservation in atoms S. A. Blundell, W. R. Johnson, and J. Sapirstein; Part II. Photoionization of Atoms: 4. Single photoionization processes J. J. Boyle, and M. D. Kutzner; 5. Photoionization dominated by double excitation T. N. Chang; 6. Direct double photoionization in atoms Z. W. Liu; 7. Photoelectron angular distributions Steven T. Manson; Part III. A. Atomic Scattering - General Considerations: 8. The many-body approach to electron-atom collisions M. Ya Amusia; 9. Theoretical aspects of electron impact ionization P. L. Altick; Part III. B. Atomic Scattering - Low-Order Applications: 10. Perturbation series methods D. H. Madison; 11. Target dependence of the triply differential cross section Cheng Pan and Anthony F. Starace; 12. Overview of Thomas processes for fast mass transfer J. H. McGuire, Jack C. Straton and T. Ishihara; Part III. C. Atomic Scattering - All-Order Applications: 13. R-matrix Theory: Some Recent Applications Philip G. Burke: 14. Electron scattering: application of Dirac R-matrix theory Wasantha Wijesundera, Ian Grant and Patrick Norrington; 15. Close coupling and distorted-wave theory D. C. Griffin and M. S. Pindzola; Appendix: Units and notation; References; Index.
NASA Astrophysics Data System (ADS)
Boyle, J. J.; Pindzola, M. S.
1998-09-01
Preface; Contributors; Introduction; Part I. Atomic Structure: 1. Development of atomic many-body theory Ingvar Lindgren; 2. Relativistic MBPT for highly charged ions W. R. Johnson; 3. Parity nonconservation in atoms S. A. Blundell, W. R. Johnson, and J. Sapirstein; Part II. Photoionization of Atoms: 4. Single photoionization processes J. J. Boyle, and M. D. Kutzner; 5. Photoionization dominated by double excitation T. N. Chang; 6. Direct double photoionization in atoms Z. W. Liu; 7. Photoelectron angular distributions Steven T. Manson; Part III. A. Atomic Scattering - General Considerations: 8. The many-body approach to electron-atom collisions M. Ya Amusia; 9. Theoretical aspects of electron impact ionization P. L. Altick; Part III. B. Atomic Scattering - Low-Order Applications: 10. Perturbation series methods D. H. Madison; 11. Target dependence of the triply differential cross section Cheng Pan and Anthony F. Starace; 12. Overview of Thomas processes for fast mass transfer J. H. McGuire, Jack C. Straton and T. Ishihara; Part III. C. Atomic Scattering - All-Order Applications: 13. R-matrix Theory: Some Recent Applications Philip G. Burke: 14. Electron scattering: application of Dirac R-matrix theory Wasantha Wijesundera, Ian Grant and Patrick Norrington; 15. Close coupling and distorted-wave theory D. C. Griffin and M. S. Pindzola; Appendix: Units and notation; References; Index.
Many-body localization nonlinear transport
Fominov, Yakov
Many-body localization and nonlinear transport in disordered conductors D. M. Basko I. L. Aleiner B is softened, but not sufficiently #12;Anderson localization in the many-body Fock space many-body Fock states. Aleiner, and B. Altshuler, Annals of Physics 321, 1126 (2006) #12;one-body many-body localized in space
Tensor network states for the description of quantum many-body systems
Thorsten B. Wahl
2015-09-20
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the corresponding state has some kind of non-local hidden order. We give examples fulfilling this criterion and eventually use it to obtain all such MPS with bond dimension 2 and 3. In the second part, we show that Projected Entangled Pair States (PEPS) in two spatial dimensions can describe chiral topological states by explicitly constructing a family of such states with a non-trivial Chern number. We demonstrate that such free fermionic PEPS must necessarily be non-injective and have gapless parent Hamiltonians. Moreover, we provide numerical evidence that they can nevertheless approximate well the physical properties of Chern insulators with local Hamiltonians at arbitrary temperatures. We also construct long range, topological Hamiltonians with a flat energy spectrum for which those PEPS are unique ground states. As for non-chiral topological PEPS, the non-trivial, topological properties can be traced down to the existence of a symmetry on the virtual level of the PEPS tensor that is used to build the state. We use the special properties of PEPS to build the boundary theory and show how the symmetry results in the appearance of chiral modes, a ground state degeneracy of the parent Hamiltonian on the torus and a universal correction to the area law for the zero R\\'enyi entropy. Finally, we show that PEPS can also describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry of the PEPS tensor that gives rise to the global topological character. We also extract characteristic quantities of the edge Conformal Field Theory using the bulk-boundary correspondence.
On some nonlinear partial differential equations for classical and quantum many body systems
Marahrens, Daniel
2012-11-13
of this approach. First, without worrying about regularity, we set ?(f) = F (?f, ??) for any function or distribution f on Td. The function ? can be turned into a function of the empirical measure by employing the map piN defined by (piN?)(?) = ?(µN? ) for all ?... -dimensional NLS is usually obtained as an approximation of the three-dimensional NLS in the case of a strongly confining potential (a disc-shaped condensate). Hence we shall consider both cases d = 2, 3. So far this equation has only been considered in [37, 38...
NASA Astrophysics Data System (ADS)
Sliusarenko, O. Yu.; Chechkin, A. V.; Slyusarenko, Yu. V.
2015-04-01
By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton's equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the single-particle distribution function, we use a regular cutoff procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field. Within this approximation, we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases are discussed by assuming either Gaussian statistics of external perturbation or homogeneity of the system.
Many-body coherent destruction of tunneling in photonic lattices
Stefano Longhi
2011-11-15
An optical realization of the phenomenon of many-body coherent destruction of tunneling, recently predicted for interacting many-boson systems by Gong, Molina and Haenggi [Phys. Rev. Lett. 103, 133002 (2009)], is proposed for light transport in engineered waveguide arrays. The optical system enables a direct visualization in Fock space of the many-body tunneling control process
Many-body coherent destruction of tunneling in photonic lattices
Longhi, Stefano [Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, I-20133 Milano (Italy)
2011-03-15
An optical realization of the phenomenon of many-body coherent destruction of tunneling, recently predicted for interacting many-boson systems by Gong, Molina, and Haenggi [Phys. Rev. Lett. 103, 133002 (2009)], is proposed for light transport in engineered waveguide arrays. The optical system enables a direct visualization in Fock space of the many-body tunneling control process.
G. Carmi; D. Bohm
1964-01-01
We continue the development started in the preceding paper, in which we treated the many-body problem by separating the motion into an oscillatory part deltaxi, deltapi, and a nonoscillatory part Xi, Pi, the latter being obtained by a noncanonical transformation from xi, pi which is just so tailored as to project out the oscillatory features from xi, pi, and thereby
Many-Body Models for Molecular Nanomagnets
NASA Astrophysics Data System (ADS)
Chiesa, A.; Carretta, S.; Santini, P.; Amoretti, G.; Pavarini, E.
2013-04-01
We present a flexible and effective ab initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as a one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni, and the single-molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.
Construction and Analysis of a Many-Body Neutrino model
NASA Astrophysics Data System (ADS)
Okuniewicz, Ivona
2009-03-01
In systems such as the early universe and supernova neutrinos comprise a large fraction of the total particle number density thus one needs to consider neutrino self-refraction. Coherent neutrino-neutrino scattering has been found to play a role in the flavour evolution of the system. Traditionally this problem has been analysed by assuming that the wavefunction of the system can be factorised into one-body states. However in 1992 Pantaleone showed that a neutrino ensemble is in general a many-body problem due to the off-diagonal contribution to the neutrino refractive index. This topic was unexamined until recently. It has been suggested by Bell, Rawlinson and Sawyer that quantum entanglement could play an essential role in the flavour evolution of the dense neutrino system. In this thesis we examine the validity of the one-body approximation by constructing a many-body neutrino model. The neutrino system is modelled by a system of interacting spins following earlier work of Friedland and Lunardini. We extend this work by generalising the model to initial states with asymmetric flavour composition. We find an exact analytical solution to the system. The investigation has revealed an array of interesting physics including semi-classical behaviour, quantum equilibration and a transition from semi-classical to purely quantum regimes. Further, this study has found no evidence for the violation of the one-body description of a dense neutrino ensemble. We also note that our analysis is valid for any two state system with equal strength interactions.
Ogawa, Y.; Minami, F.
2013-12-04
We show the coherent control of dephasing process of exciton polarization due to heavy hole-heavy hole and heavy hole-light hole scatterings in a GaAs single quantum well. The memory time of the exction scattering is estimated as 0.47 ps.
Interferometric probes of many-body localization.
Serbyn, M; Knap, M; Gopalakrishnan, S; Papi?, Z; Yao, N Y; Laumann, C R; Abanin, D A; Lukin, M D; Demler, E A
2014-10-01
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems. PMID:25325656
Many-body fits of phase-equivalent effective interactions
Calvin W. Johnson
2010-09-20
In many-body theory it is often useful to renormalize short-distance, high-momentum components of an interaction via unitary transformations. Such transformations preserve the on-shell physical observables of the two-body system (mostly phase-shifts, hence unitarily-connected effective interactions are often called phase-equivalent), while modifying off-shell T-matrix elements influential in many-body systems. In this paper I lay out a general and systematic approach for controlling the off-shell behavior of an effective interaction, which can be adjusted to many-body properties, and present an application to trapped fermions at the unitary
Many-body localization as percolation in d >1
NASA Astrophysics Data System (ADS)
Chandran, Anushya; Laumann, Chris; Gottesman, Daniel
2015-03-01
Statistical mechanics is the framework that connects thermodynamics to the microscopic world. It hinges on the assumption of equilibration. Isolated quantum systems need not equilibrate; this is the phenomenon of many-body localization (MBL). While a detailed understanding of MBL and the associated delocalization transition is beginning to emerge in one dimension, relatively little is known about higher dimensions. In this work, we present a minimal tractable model for MBL in all spatial dimensions. Specifically, we analyze a disordered Floquet circuit composed of Clifford gates. In one dimension, the system is always localized, while in higher dimensions, it exhibits both delocalized and localized phases. The localized phase consists of well-defined metallic puddles embedded in an insulating matrix. When the puddles percolate, the system delocalizes; this maps the dynamical transition to critical percolation. We also comment on the stability of the phases to generic perturbations away from the Clifford class.
Aiming for benchmark accuracy with the many-body expansion.
Richard, Ryan M; Lao, Ka Un; Herbert, John M
2014-09-16
Conspectus The past 15 years have witnessed an explosion of activity in the field of fragment-based quantum chemistry, whereby ab initio electronic structure calculations are performed on very large systems by decomposing them into a large number of relatively small subsystem calculations and then reassembling the subsystem data in order to approximate supersystem properties. Most of these methods are based, at some level, on the so-called many-body (or "n-body") expansion, which ultimately requires calculations on monomers, dimers, ..., n-mers of fragments. To the extent that a low-order n-body expansion can reproduce supersystem properties, such methods replace an intractable supersystem calculation with a large number of easily distributable subsystem calculations. This holds great promise for performing, for example, "gold standard" CCSD(T) calculations on large molecules, clusters, and condensed-phase systems. The literature is awash in a litany of fragment-based methods, each with their own working equations and terminology, which presents a formidable language barrier to the uninitiated reader. We have sought to unify these methods under a common formalism, by means of a generalized many-body expansion that provides a universal energy formula encompassing not only traditional n-body cluster expansions but also methods designed for macromolecules, in which the supersystem is decomposed into overlapping fragments. This formalism allows various fragment-based methods to be systematically classified, primarily according to how the fragments are constructed and how higher-order n-body interactions are approximated. This classification furthermore suggests systematic ways to improve the accuracy. Whereas n-body approaches have been thoroughly tested at low levels of theory in small noncovalent clusters, we have begun to explore the efficacy of these methods for large systems, with the goal of reproducing benchmark-quality calculations, ideally meaning complete-basis CCSD(T). For high accuracy, it is necessary to deal with basis-set superposition error, and this necessitates the use of many-body counterpoise corrections and electrostatic embedding methods that are stable in large basis sets. Tests on small noncovalent clusters suggest that total energies of complete-basis CCSD(T) quality can indeed be obtained, with dramatic reductions in aggregate computing time. On the other hand, naive applications of low-order n-body expansions may benefit from significant error cancellation, wherein basis-set superposition error partially offsets the effects of higher-order n-body terms, affording fortuitously good results in some cases. Basis sets that afford reasonable results in small clusters behave erratically in larger systems and when high-order n-body expansions are employed. For large systems, and (H2O)N?30 is large enough, the combinatorial nature of the many-body expansion presents the possibility of serious loss-of-precision problems that are not widely appreciated. Tight thresholds are required in the subsystem calculations in order to stave off size-dependent errors, and high-order expansions may be inherently numerically ill-posed. Moreover, commonplace script- or driver-based implementations of the n-body expansion may be especially susceptible to loss-of-precision problems in large systems. These results suggest that the many-body expansion is not yet ready to be treated as a "black-box" quantum chemistry method. PMID:24883986
Dynamical Stability of a Many-body Kapitza Pendulum
Roberta Citro; Emanuele G. Dalla Torre; Luca DÁlessio; Anatoli Polkovnikov; Mehrtash Babadi; Takashi Oka; Eugene Demler
2015-01-22
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the effective Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculations. Classical and quantum experiments are proposed to verify the validity of our results.
Many-Body Dispersion Interactions in Molecular Materials
NASA Astrophysics Data System (ADS)
Distasio, Robert A., Jr.
2015-03-01
In this work, we have developed an efficient method for obtaining an accurate theoretical description of van der Waals (vdW) interactions that includes both long-range Coulomb electrodynamic response screening effects as well as treatment of the many-body vdW energy to infinite order. This method goes beyond the standard C6 /R6 pairwise additive approximation and can easily be coupled to a wide array of theoretical methods, ranging from classical force fields to higher-level quantum chemical calculations. To demonstrate the increasingly important role played by many-body vdW interactions in large, structurally complex molecular systems, we use this method to investigate several pertinent molecular properties, such as binding energies/affinities in gas-phase molecular dimers and supramolecular complexes, relative conformational energetics in small polypeptides, and thermodynamic stabilities among competing molecular crystal polymorphs. This work received funding from the Department of Energy under Grant Nos.: DOE DE-SC0008626 and DOE DE-FG02ER46201 and the European Research Council (ERC Starting Grant VDW-CMAT).
Similarity renormalization group to the many-body problems
NASA Astrophysics Data System (ADS)
Tsukiyama, Koshiroh; Bogner, Scott; Schwenk, Achim
2009-10-01
One of the major goals of nuclear structure theory is to explain many-body phenomena from nucleonic interactions. Since realistic nucleon-nucleon interactions have strong repulsion and tensor component at short distance, nuclear system is non-perturbative and even few-body problems are difficult to solve. Several methods based on renormalization group (RG) or unitary transformation can be used to treat the short-range correlation, the consequence of which nuclear many-body calculations converge rapidly. These methods, however, generate many-body forces which significantly affects the observable unless the induced forces are treated properly. To overcome this problem, one way is to keep the induced many-body forces explicitly. We propose an alternative way, In-medium similarity renormalization group (SRG), by extending the free-space SRG. We derive the flow equations for normal-ordered Hamiltonian assuming a core so that the dominant part of many-body correlations are incorporated into density dependent lower-body forces, driving the Hamiltonian more feasible form for the many-body calculations. In-medium SRG provides a new systematic and non-perturbative path from nucleonic interactions to the many-body calculations. We will show the newest results of the methods.
Towards Efficient and General Method for Many-Body van-der-Waals Interactions
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2012-02-01
Van der Waals interactions are intrinsically many-body phenomena, arising from collective electron fluctuations in a given material. Adiabatic connection fluctuation-dissipation theorem (ACFDT) allows to compute the many-body vdW interactions accurately. However, the ACFDT computational cost is prohibitive for real materials, even when the random-phase approximation is employed for the response function. We show how the problem of computing the long-range many-body vdW energy for real systems can be solved efficiently by mapping the system (molecule or condensed matter) onto a collection of quantum harmonic oscillators. Currently, our method, which couples density-functional theory with the many-body dispersion energy (DFT+MBD), is developed for non-metallic system [A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, submitted]. The DFT+MBD method includes the hybridization effects by using the Tkatchenko-Scheffler approach [PRL 102, 073005 (2009)], the long-range Coulomb screening through classical electrodynamics [B. U. Felderhof, Physica 29, 1569 (1974)], and the many-body vdW energy from the coupled-fluctuating dipole model [M. W. Cole et al., Mol. Simul. 35, 849 (2009)]. The successes of the DFT+MBD approach and the many challenges that lie ahead will be discussed.
Relativistically Covariant Many-Body Perturbation Procedure
NASA Astrophysics Data System (ADS)
Lindgren, Ingvar; Salomonson, Sten; Hedendahl, Daniel
A covariant evolution operator (CEO) can be constructed, representing the time evolution of the relativistic wave unction or state vector. Like the nonrelativistic version, it contains (quasi-)singularities. The regular part is referred to as the Green’s operator (GO), which is the operator analogue of the Green’s function (GF). This operator, which is a field-theoretical concept, is closely related to the many-body wave operator and effective Hamiltonian, and it is the basic tool for our unified theory. The GO leads, when the perturbation is carried to all orders, to the Bethe-Salpeter equation (BSE) in the equal-time or effective-potential approximation. When relaxing the equal-time restriction, the procedure is fully compatible with the exact BSE. The calculations are performed in the photonic Fock space, where the number of photons is no longer constant. The procedure has been applied to helium-like ions, and the results agree well with S-matrix results in cases when comparison can be performed. In addition, evaluation of higher-order quantum-electrodynamical (QED) correlational effects has been performed, and the effects are found to be quite significant for light and medium-heavy ions.
Many body population trapping in ultracold dipolar gases
NASA Astrophysics Data System (ADS)
Dutta, Omjyoti; Lewenstein, Maciej; Zakrzewski, Jakub
2014-05-01
A system of interacting dipoles is of paramount importance for understanding many-body physics. The interaction between dipoles is anisotropic and long-range. While the former allows one to observe rich effects due to different geometries of the system, long-range (1/{{r}^{3}}) interactions lead to strong correlations between dipoles and frustration. In effect, interacting dipoles in a lattice form a paradigmatic system with strong correlations and exotic properties with possible applications in quantum information technologies, and as quantum simulators of condensed matter physics, material science, etc. Notably, such a system is extremely difficult to model due to a proliferation of interaction induced multi-band excitations for sufficiently strong dipole-dipole interactions. In this article we develop a consistent theoretical model of interacting polar molecules in a lattice by applying the concepts and ideas of ionization theory which allows us to include highly excited Bloch bands. Additionally, by involving concepts from quantum optics (population trapping), we show that one can induce frustration and engineer exotic states, such as Majumdar-Ghosh state, or vector-chiral states in such a system.
Non equilibrium dissipation-driven steady many-body entanglement
Bruno Bellomo; Mauro Antezza
2015-04-03
We study an ensemble of two-level quantum systems (qubits) interacting with a common electromagnetic field in proximity of a dielectric slab whose temperature is held different from that of some far surrounding walls. We show that the dissipative dynamics of the qubits driven by this stationary and out of thermal equilibrium (OTE) field, allows the production of steady many-body entangled states, differently from the case at thermal equilibrium where steady states are always non-entangled. By studying up to ten qubits, we point out the role of symmetry in the entanglement production, which is exalted in the case of permutationally invariant configurations. In the case of three qubits, we find a strong dependence of tripartite entanglement on the spatial disposition of the qubits, and in the case of six qubits, we find several highly entangled bipartitions where entanglement can, remarkably, survive for large qubit-qubit distances up to 100 $\\mu$m.
Nonequilibrium dissipation-driven steady many-body entanglement
NASA Astrophysics Data System (ADS)
Bellomo, Bruno; Antezza, Mauro
2015-04-01
We study an ensemble of two-level quantum systems (qubits) interacting with a common electromagnetic field in the proximity of a dielectric slab whose temperature is held different from that of some far surrounding walls. We show that the dissipative dynamics of the qubits driven by this stationary and out of thermal equilibrium field allows the production of steady many-body entangled states, different from the case at thermal equilibrium where steady states are always nonentangled. By studying up to ten qubits, we point out the role of symmetry in the entanglement production, which is exalted in the case of permutationally invariant configurations. In the case of three qubits, we find a strong dependence of tripartite entanglement on the spatial disposition of the qubits, and in the case of six qubits we find several highly entangled bipartitions where entanglement can, remarkably, survive for large qubit-qubit distances up to 100 ? m .
Many-body dynamics of a BEC quenched to unitarity
NASA Astrophysics Data System (ADS)
Corson, John; Sykes, Andrew; D'Incao, Jose; Koller, Andrew; Greene, Chris; Rey, Ana Maria; Hazzard, Kaden; Bohn, John
2014-03-01
The dynamics of a dilute BEC quenched to unitarity are studied using a variational ansatz for the many-body quantum state. Despite the resonant atom-atom interactions, the condensate does not deplete instantaneously, and this allows for a self-consistent mean-field-like description of the system at short (but experimentally-accessible) times. At infinite scattering length and zero temperature, the dynamics are found to scale universally with the number density, as reported in the experiment of Makotyn et al, arXiv1308.3696. We predict the time evolution of observables such as the momentum distribution nk(t) , the contact C(t) , and the density nm(t) of Feshbach molecules generated by the interaction quench. We observe a saturation of large-momentum populations on a time scale that is consistent with recent measurements.
Novel solvable variants of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-02-01
A recent technique to identify solvable many-body problems in two-dimensional space yields, via a new twist, new many-body problems of "goldfish" type. Some of these models are isochronous, namely their generic solutions are completely periodic with a fixed period (independent of the initial data). The investigation of the behavior of some of these isochronous systems in the vicinity of their equilibrium configurations yields some amusing diophantine relations.
Many-body applications of the stochastic limit: a review
F. Bagarello
2009-04-01
We review some applications of the perturbative technique known as the {\\em stochastic limit approach} to the analysis of the following many-body problems: the fractional quantum Hall effect, the relations between the Hepp-Lieb and the Alli-Sewell models (as possible models of interaction between matter and radiation), and the open BCS model of low temperature superconductivity.
Many body theory of stochastic gene expression
NASA Astrophysics Data System (ADS)
Walczak, Aleksandra M.
The regulation of expression states of genes in cells is a stochastic process. The relatively small numbers of protein molecules of a given type present in the cell and the nonlinear nature of chemical reactions result in behaviours, which are hard to anticipate without an appropriate mathematical development. In this dissertation, I develop theoretical approaches based on methods of statistical physics and many-body theory, in which protein and operator state dynamics are treated stochastically and on an equal footing. This development allows me to study the general principles of how noise arising on different levels of the regulatory system affects the complex collective characteristics of systems observed experimentally. I discuss simple models and approximations, which allow for, at least some, analytical progress in these problems. These have allowed us to understand how the operator state fluctuations may influence the steady state properties and lifetimes of attractors of simple gene systems. I show, that for fast binding and unbinding from the DNA, the operator state may be taken to be in equilibrium for highly cooperative binding, when predicting steady state properties as is traditionally done. Nevertheless, if proteins are produced in bursts, the DNA binding state fluctuations must be taken into account explicitly. Furthermore, even when the steady state probability distributions are weakly influenced by the operator state fluctuations, the escape rate in biologically relevant regimes strongly depends on transcription factor-DNA binding rates.
Symmetry-protected many-body Aharonov-Bohm effect
Luiz H. Santos; Juven Wang
2014-08-19
It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path - the Aharonov-Bohm effect. Here we examine an Aharonov-Bohm effect on a many-body wavefunction. Specifically, we study this many-body effect on the gapless edge states of a bulk gapped phase protected by a global symmetry (such as $\\mathbb{Z}_{N}$) - the symmetry-protected topological (SPT) states. The many-body analogue of spectral shifts, the twisted wavefunction and the twisted boundary realization are identified in this SPT state. An explicit lattice construction of SPT edge states is derived, and a challenge of gauging its non-onsite symmetry is overcome. Agreement is found in the twisted spectrum between a numerical lattice calculation and a conformal field theory prediction.
Local reversibility and entanglement structure of many-body ground states
Kuwahara, Tomotaka; Amico, Luigi; Vedral, Vlatko
2015-01-01
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are ...
How to detect many body localization in experiments
NASA Astrophysics Data System (ADS)
Nandkishore, Rahul
2015-03-01
The standard theory of many body localization (MBL) is framed in terms of exact eigenstates of perfectly isolated quantum systems. However, exact eigenstates can neither be prepared nor measured in the laboratory, and perfectly isolated quantum systems are equally unrealizable. In this talk I explain how MBL can be reformulated without invoking exact eigenstates or perfect isolation. I introduce a way to think about MBL in terms of correlation functions of local operators, evaluated in arbitrary states. This perspective reformulates the standard theory in terms of (in principle) experimentally measurable quantities. Moreover, this ``spectral'' perspective on MBL is far more robust than the conventional ``eigenstate'' perspective. Eigenstates thermalize upon arbitrarily weak coupling to an external environment, but the correlation functions (which are the physical observables) continue to show signatures of MBL as long as the coupling to the environment is weaker than the characteristic energy scales in the system Hamiltonian. I also show how this ``spectral perspective'' can be used to reveal additional structure in the MBL phase, and to make progress on otherwise intractable theory problems. Collaborators: Sarang Gopalakrishnan, David Huse, Sonika Johri, Ravin Bhatt.
Spatially partitioned many-body vortices
Shachar Klaiman; Ofir E. Alon
2014-12-14
A vortex in Bose-Einstein condensates is a localized object which looks much like a tiny tornado storm. It is well described by mean-field theory. In the present work we go beyond the current paradigm and introduce many-body vortices. These are made of {\\it spatially-partitioned} clouds, carry definite total angular momentum, and are fragmented rather than condensed objects which can only be described beyond mean-field theory. A phase diagram based on a mean-field model assists in predicting the parameters where many-body vortices occur. Implications are briefly discussed.
Many-body singlets by dynamic spin polarization
Wang Yao
2011-01-20
We show that dynamic spin polarization by collective raising and lowering operators can drive a spin ensemble from arbitrary initial state to many-body singlets, the zero-collective-spin states with large scale entanglement. For an ensemble of $N$ arbitrary spins, both the variance of the collective spin and the number of unentangled spins can be reduced to O(1) (versus the typical value of O(N)), and many-body singlets can be occupied with a population of $\\sim 20 %$ independent of the ensemble size. We implement this approach in a mesoscopic ensemble of nuclear spins through dynamic nuclear spin polarization by an electron. The result is of two-fold significance for spin quantum technology: (1) a resource of entanglement for nuclear spin based quantum information processing; (2) a cleaner surrounding and less quantum noise for the electron spin as the environmental spin moments are effectively annihilated.
Symmetries and self-similarity of many-body wavefunctions
Piotr Migda?
2014-12-21
This PhD thesis is dedicated to the study of the interplay between symmetries of quantum states and their self-similar properties. It consists of three connected threads of research: polynomial invariants for multiphoton states, visualization schemes for quantum many-body systems and a complex networks approach to quantum walks on a graph. First, we study the problem of which many-photon states are equivalent up to the action of passive linear optics. We prove that it can be converted into the problem of equivalence of two permutation-symmetric states, not necessarily restricted to the same operation on all parties. We show that the problem can be formulated in terms of symmetries of complex polynomials of many variables, and provide two families of invariants, which are straightforward to compute and provide analytical results. Second, we study a family of recursive visualization schemes for many-particle systems, for which we have coined the name 'qubism'. While all many-qudit states can be plotted with qubism, it is especially useful for spin chains and one-dimensional translationally invariant states. This symmetry results in self-similarity of the plot, making it more comprehensible and allowing to discover certain structures. Third, we study quantum walks of a single particle on graphs, which are classical analogues of random walks. Our focus is on the long-time limit of the probability distribution and we study how (especially in the long-time limit) off-diagonal elements of the density matrix behave. We use them to perform quantum community detection - splitting of a graph into subgraphs in such a way that the coherence between them is small. Our method captures properties that classical methods cannot - the impact of constructive and destructive interference, as well as the dependence of the results on the tunneling phase.
Many-Body Characterization of Particle-Conserving Topological Superfluids
NASA Astrophysics Data System (ADS)
Ortiz, Gerardo; Dukelsky, Jorge; Cobanera, Emilio; Esebbag, Carlos; Beenakker, Carlo
2014-12-01
What distinguishes trivial superfluids from topological superfluids in interacting many-body systems where the number of particles is conserved? Building on a class of integrable pairing Hamiltonians, we present a number-conserving, interacting variation of the Kitaev model, the Richardson-Gaudin-Kitaev chain, that remains exactly solvable for periodic and antiperiodic boundary conditions. Our model allows us to identify fermion parity switches that distinctively characterize topological superconductivity (fermion superfluidity) in generic interacting many-body systems. Although the Majorana zero modes in this model have only a power-law confinement, we may still define many-body Majorana operators by tuning the flux to a fermion parity switch. We derive a closed-form expression for an interacting topological invariant and show that the transition away from the topological phase is of third order.
Goldfishing: A new solvable many-body problem
NASA Astrophysics Data System (ADS)
Bruschi, M.; Calogero, F.
2006-10-01
A recent technique allows one to identify and investigate solvable dynamical systems naturally interpretable as classical many-body problems, being characterized by equations of motion of Newtonian type (generally in two-dimensional space). In this paper we tersely review results previously obtained in this manner and present novel findings of this kind: mainly solvable variants of the goldfish many-body model, including models that feature isochronous classes of completely periodic solutions. Different formulations of these models are presented. The behavior of one of these isochronous dynamical systems in the neighborhood of its equilibrium configuration is investigated, and in this manner some remarkable Diophantine findings are obtained.
Apkarian, V. Ara
of diatomics-in-ionic-systems: Applied to HF clusters M. Ovchinnikov and V. A. Apkariana) Department February 1999 A perturbative extension of the diatomics-in-ionic-systems DIIS is formulated as a practical. The approach allows the analysis of H-bonding and its nonadditive induction and dispersion forces in terms
Torquato, Salvatore
of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 276957910 S of the microstructure of many- particle systems such as random heterogeneous materials (e.g., suspensions, composites
NASA Astrophysics Data System (ADS)
McNanna, Mitch A.; Caprio, Mark A.
2014-09-01
Natural orbitals have been applied in atomic and molecular electronic-structure theory to increase the accuracy of calculations of observables for a many-particle system. However, unlike the electron-structure problem, the nuclear problem is translationally invariant. We created a testbed code to test the usefulness of natural orbitals as they may apply to translationally invariant problems. The relative Hamiltonian matrix of a two-particle system in one dimension is first calculated in a basis of antisymmetrized products of the harmonic oscillator eigenfunctions. The natural orbitals are then calculated for the resulting ground state, and the Hamiltonian matrix is recalculated using a two-particle basis built from the natural orbitals. The effect of basis size on the accuracy of the ground state energy calculation is explored. Natural orbitals have been applied in atomic and molecular electronic-structure theory to increase the accuracy of calculations of observables for a many-particle system. However, unlike the electron-structure problem, the nuclear problem is translationally invariant. We created a testbed code to test the usefulness of natural orbitals as they may apply to translationally invariant problems. The relative Hamiltonian matrix of a two-particle system in one dimension is first calculated in a basis of antisymmetrized products of the harmonic oscillator eigenfunctions. The natural orbitals are then calculated for the resulting ground state, and the Hamiltonian matrix is recalculated using a two-particle basis built from the natural orbitals. The effect of basis size on the accuracy of the ground state energy calculation is explored. Supported by the US NSF under grant NSF-PHY05-52843, the US DOE under grant DE-FG02-95ER-4093 and the Research Corporation for Science Advancement under a Cottrell Scholar Award.
Approximating many-body induction to efficiently describe molecular liquids
Herbert, John
as the structures and properties of molecular systems. This study focuses on approximating many-body electronic, or polarization. We construct a single electron potential in which the coarse grained electronic degrees this into the description of the single molecular frag- ments. The fragments are then coupled to one another through
Solving the many body pairing problem through Monte Carlo methods
NASA Astrophysics Data System (ADS)
Lingle, Mark; Volya, Alexander
2012-03-01
Nuclear superconductivity is a central part of quantum many-body dynamics. In mesoscopic systems such as atomic nuclei, this phenomenon is influenced by shell effects, mean-field deformation, particle decay, and by other collective and chaotic components of nucleon motion. The ability to find an exact solution to these pairing correlations is of particular importance. In this presentation we develop and investigate the effectiveness of different methods of attacking the nucleon pairing problem in nuclei. In particular, we concentrate on the Monte Carlo approach. We review the configuration space Monte Carlo techniques, the Suzuki-Trotter breakup of the time evolution operator, and treatment of the pairing problem with non-constant matrix elements. The quasi-spin symmetry allows for a mapping of the pairing problem onto a problem of interacting spins which in turn can be solved using a Monte Carlo approach. The algorithms are investigated for convergence to the true ground state of model systems and calculated ground state energies are compared to those found by an exact diagonalization method. The possibility to include other non-pairing interaction components of the Hamiltonian is also investigated.
Many-Body Localization Implies that Eigenvectors are Matrix-Product States.
Friesdorf, M; Werner, A H; Brown, W; Scholz, V B; Eisert, J
2015-05-01
The phenomenon of many-body localization has received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at nonzero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalization following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties--a vanishing group velocity and the absence of transport--with entanglement properties of individual eigenvectors. For systems with a generic spectrum, we prove that strong dynamical localization implies that all of its many-body eigenvectors have clustering correlations. The same is true for parts of the spectrum, thus allowing for the existence of a mobility edge above which transport is possible. In one dimension these results directly imply an entanglement area law; hence, the eigenvectors can be efficiently approximated by matrix-product states. PMID:25978216
Reboredo, Fernando A [ORNL
2012-01-01
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\\bf 79}, 195117 (2009), Reboredo, {\\it ibid.} {\\bf 80}, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. A recursive optimization algorithm is derived from the time evolution of the mixed probability density. The mixed probability density is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weigh allows the amplitude of the fix-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC and the fixed-phase approximation [Ortiz, Ceperley and Martin Phys Rev. Lett. {\\bf 71}, 2777 (1993)]. When used recursively it improves simultaneously the node and phase. The algorithm is demonstrated to converge to the nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The method is also applied to obtain low energy excitations with magnetic field or periodic boundary conditions. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.
Gravitation as a Many Body Problem
Pawel O. Mazur
1997-08-25
The idea of viewing gravitation as a many body phenomenon is put forward here. Physical arguments supporting this idea are briefly reviewed. The basic mathematical object of the new gravitational mechanics is a matrix of operators. Striking similarity of the method of R-matrix (QISM) to the mathematical formulation of the new gravitational mechanics is pointed out. The s-wave difference Schrodinger equation describing a process of emission of radiation by a gravitating particle is shown to be analogous to the Baxter equation of the QISM.
Amusia, M.Ya. [Argonne National Lab., IL (United States)]|[A.F. Ioffe Physical-Technical Institute, St. Petersburg (Russian Federation)
1995-01-01
The author presents this article in the volume, dedicated to the 70th birthday of Academician S. T. Belyaev. He has known him personally since 1961 and admires his profound contributions to the theory of Bose-liquids, to the theory of superconductivity of atomic nuclei and some other important scientific works. Belyaev is well known also as an organizer of science and education. For years he was, and is still the Chairman of the Synchrotron Radiation Commission of the Russian Academy of Science, a body which was established long ago to promote construction of high intensity light sources, and technological as well as scientific research using this light. One of the important directions of this study is investigation of photoabsorbtion by multielectron atoms in order to obtain information about their structure.
On the simulation of indistinguishable fermions in the many-body Wigner formalism
Sellier, J.M. Dimov, I.
2015-01-01
The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.
On the simulation of indistinguishable fermions in the many-body Wigner formalism
NASA Astrophysics Data System (ADS)
Sellier, J. M.; Dimov, I.
2015-01-01
The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange-correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi-Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.
Non-equilibrium many body dynamics
Creutz, M.; Gyulassy, M.
1997-09-22
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop.
Herbert, John
clusters, halide-water clusters, a methane clathrate hydrate, and a DNA intercalation complex illustrate such as molecular and ionic clusters, molecular crystals, clathrates, or protein-ligand complexes. As in traditional
Machine learning for many-Body physics
NASA Astrophysics Data System (ADS)
Arsenault, Louis-Francois; Lopez-Bezanilla, Alejandro; von Lilienfeld, O. Anatole; Millis, Andrew J.
2015-03-01
We investigate the application to many-body physics of Machine Learning (ML) methods for predicting new results from accumulated knowledge. We show that ML can be used efficiently for the Anderson impurity model (AIM) and present preliminary results on its use as a solver for dynamical mean field theory (DMFT). We establish that the best representation of the Green's function for ML is by parametrizing it as an expansion in term of Legendre polynomials. In DMFT applications, a key issue is the choice of descriptor, the data representation used as input for ML, which is not dependent on the impurity solver. Different parametrizations are examined. The ability to distinguish metallic and Mott insulating solutions is analysed. DOE No. 3F-3138.
Many-body theory of surface-enhanced Raman scattering
Masiello, David J
2008-01-01
A many-body Green's function approach to the microscopic theory of surface-enhanced Raman scattering is presented. Interaction effects between a general molecular system and a spatially anisotropic metal particle supporting plasmon excitations in the presence of an external radiation field are systematically included through many-body perturbation theory. Reduction of the exact effects of molecular-electronic correlation to the level of Hartree-Fock mean-field theory is made for practical initial implementation, while description of collective oscillations of conduction electrons in the metal is reduced to that of a classical plasma density; extension of the former to a Kohn-Sham density-functional or second-order M{\\o}ller-Plesset perturbation theory is discussed; further specialization of the latter to the random-phase approximation allows for several salient features of the formalism to be highlighted without need for numerical computation. Scattering and linear-response properties of the coupled system su...
Simulating typical entanglement with many-body Hamiltonian dynamics
Nakata, Yoshifumi [Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan); Murao, Mio [Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033 (Japan); Institute for Nano Quantum Information Electronics, University of Tokyo, Tokyo 153-8505 (Japan)
2011-11-15
We study the time evolution of the amount of entanglement generated by one-dimensional spin-1/2 Ising-type Hamiltonians composed of many-body interactions. We investigate sets of states randomly selected during the time evolution generated by several types of time-independent Hamiltonians by analyzing the distributions of the amount of entanglement of the sets. We compare such entanglement distributions with that of typical entanglement, entanglement of a set of states randomly selected from a Hilbert space with respect to the unitarily invariant measure. We show that the entanglement distribution obtained by a time-independent Hamiltonian can simulate the average and standard deviation of the typical entanglement, if the Hamiltonian contains suitable many-body interactions. We also show that the time required to achieve such a distribution is polynomial in the system size for certain types of Hamiltonians.
Semiclassical limit for the many-body localization transition
NASA Astrophysics Data System (ADS)
Chandran, Anushya; Laumann, C. R.
2015-07-01
We introduce a semiclassical limit for many-body localization in the absence of global symmetries. Microscopically, this limit is realized by disordered Floquet circuits composed of Clifford gates. In d =1 , the resulting dynamics are always many-body localized with a complete set of strictly local integrals of motion. In d ?2 , the system realizes both localized and delocalized phases separated by a continuous transition in which ergodic puddles percolate. We argue that the phases are stable to deformations away from the semiclassical limit and estimate the resulting phase boundary. The Clifford circuit model is a distinct tractable limit from that of free fermions and suggests bounds on the critical exponents for the generic transition.
Purification and many-body localization in cold atomic gases.
Andraschko, Felix; Enss, Tilman; Sirker, Jesko
2014-11-21
We propose to observe many-body localization in cold atomic gases by realizing a Bose-Hubbard chain with binary disorder and studying its nonequilibrium dynamics. In particular, we show that measuring the difference in occupation between even and odd sites, starting from a prepared density-wave state, provides clear signatures of localization. Furthermore, we confirm as hallmarks of the many-body localized phase a logarithmic increase of the entanglement entropy in time and Poissonian level statistics. Our numerical density-matrix renormalization group calculations for infinite system size are based on a purification approach; this allows us to perform the disorder average exactly, thus producing data without any statistical noise and with maximal simulation times of up to a factor 10 longer than in the clean case. PMID:25479517
High precision framework for Chaos Many-Body Engine
I. V. Grossu; C. Besliu; D. Felea; Al. Jipa
2013-12-15
In this paper we present a C# 4.0 high precision framework for simulation of relativistic many-body systems. In order to benefit from, previously developed, chaos analysis instruments, all new modules were designed to be integrated with Chaos Many-Body Engine [1,3]. As a direct application, we used 46 digits precision for analyzing the Butterfly Effect of the gravitational force in a specific relativistic nuclear collision toy-model. Trying to investigate the average Lyapunov Exponent dependency on the incident momentum, an interesting case of intermittency was noticed. Based on the same framework, other high-precision simulations are currently in progress (e.g. study on the possibility of considering, hard to detect, extremely low frequency photons as one of the dark matter components).
Müller, Markus
Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition Kartiek be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We
Physical Significance of q Deformation and Many-Body Interactions in Nuclei
K. D. Sviratcheva; C. Bahri; A. I. Georgieva; J. P. Draayer
2007-03-21
The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40q deformation plays a significant role in understanding higher-order effects in the many-body interaction.
Many-body Landau-Zener dynamics in coupled 1D Bose liquids
Yu-Ao Chen; Sebastian D. Huber; Stefan Trotzky; Immanuel Bloch; Ehud Altman
2010-03-25
The Landau-Zener model of a quantum mechanical two-level system driven with a linearly time dependent detuning has served over decades as a textbook paradigm of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2, 46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener derived a non-perturbative prediction for the transition probability between two states, which often serves as a reference point for the analysis of more complex systems. A particularly intriguing question is whether that framework can be extended to describe many-body quantum dynamics. Here we report an experimental and theoretical study of a system of ultracold atoms, offering a direct many-body generalization of the Landau-Zener problem. In a system of pairwise tunnel-coupled 1D Bose liquids we show how tuning the correlations of the 1D gases, the tunnel coupling between the tubes and the inter-tube interactions strongly modify the original Landau-Zener picture. The results are explained using a mean-field description of the inter-tube condensate wave-function, coupled to the low-energy phonons of the 1D Bose liquid.
Fragmented Many-body States of Spin-2 Bose Gas
NASA Astrophysics Data System (ADS)
Jen, Hsiang-Hua; Yip, Sungkit
2015-05-01
For a spin-1 Bose gas with ``antiferromagnetic interaction'' in zero magnetic field, the exact ground state is fragmented, consisting two-particle spin-singlets for even number of particles. While its mean-field (MF) state is polar, it is claimed that the exact ground state can be viewed as an angular average over its MF polar state, as a direct analogy to, e.g., the generation of Fock states by averaging over the relative phase of the coherent state in the case of a double well. This picture has become the common belief in the community. In this work, we demonstrate how angular-averaged MF polar states are unable to construct the exact many-body ground states in the spin-2 case. That the angular averaged MF states is the exact ground state is simply a coincidence in the spin-1 system. We address the inapplicability of the angular-averaging process, and further investigate the limitations on obtaining the exact many-body state from angular averaging of the MF cyclic state. We also show how the angular-averaged MF state deviates from the exact eigenstate by studying the two-particle density matrices. Our results overturn the common belief that the exact ground states are equivalent to angular-averaged MF states, and give a broader perspective on fragmented many-body bosonic ground states.
Many-body effects for critical Casimir forces
T. G. Mattos; L. Harnau; S. Dietrich
2013-01-28
Within mean-field theory we calculate the scaling functions associated with critical Casimir forces for a system consisting of two spherical colloids immersed in a binary liquid mixture near its consolute point and facing a planar, homogeneous substrate. For several geometrical arrangements and boundary conditions we analyze the normal and the lateral critical Casimir forces acting on one of the two colloids. We find interesting features such as a change of sign of these forces upon varying either the position of one of the colloids or the temperature. By subtracting the pairwise forces from the total force we are able to determine the many-body forces acting on one of the colloids. We have found that the many-body contribution to the total critical Casimir force is more pronounced for small colloid-colloid and colloid-substrate distances, as well as for temperatures close to criticality, where the many-body contribution to the total force can reach up to 25%.
Quantum simulations with 8?8?Sr+? ions on planar lattice traps
Lin, Ziliang (Ziliang Carter)
2008-01-01
Quantum simulations are the use of well controlled many-body quantum systems to simulate and solve other many-body quantum systems that are not understood. This thesis describes theoretical proposals and experimental ...
Dynamics at the many-body localization transition
NASA Astrophysics Data System (ADS)
Torres-Herrera, E. J.; Santos, Lea F.
2015-07-01
The isolated one-dimensional Heisenberg model with static random magnetic fields has become paradigmatic for the analysis of many-body localization. Here, we study the dynamics of this system initially prepared in a highly-excited nonstationary state. Our focus is on the probability for finding the initial state later in time, the so-called survival probability. Two distinct behaviors are identified before equilibration. At short times, the decay is very fast and equivalent to that of clean systems. It subsequently slows down and develops a power-law behavior with an exponent that coincides with the multifractal dimension of the eigenstates.
NASA Astrophysics Data System (ADS)
Beugeling, W.; Andreanov, A.; Haque, Masudul
2015-02-01
In the spectrum of many-body quantum systems appearing in condensed matter physics, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of the full eigenspectrum has grown more recently, in particular in the context of non-equilibrium questions. Wave functions of interacting lattice quantum systems can be characterized either by local observables or by global properties such as the participation ratio (PR) in a many-body basis or the entanglement between various partitions. We present a study of the PR and of the entanglement entropy (EE) between two roughly equal spatial partitions of the system, in all the eigenfunctions of local Hamiltonians. Motivated by the similarity of the PR and EE—both are generically larger in the bulk and smaller near the edges of the spectrum—we quantitatively analyze the correlation between them. We elucidate the effect of (proximity to) integrability, showing how low-entanglement and low-PR states appear also in the middle of the spectrum as one approaches integrable points. We also determine the precise scaling behaviour of the eigenstate-to-eigenstate fluctuations of the PR and EE with respect to system size and characterize the statistical distribution of these quantities near the middle of the spectrum.
Wouter Beugeling; Alexei Andreanov; Masudul Haque
2014-10-28
In the spectrum of many-body quantum systems, the low-energy eigenstates were the traditional focus of research. The interest in the statistical properties of the full eigenspectrum has grown more recently, in particular in the context of non-equilibrium questions. Wave functions of interacting lattice quantum systems can be characterized either by local observables, or by global properties such as the participation ratio (PR) in a many-body basis or the entanglement between various partitions. We present a study of the PR and of the entanglement entropy (EE) between two roughly equal spatial partitions of the system, in all the eigenfunctions of local Hamiltonians. Motivated by the similarity of the PR and EE - both are generically larger in the bulk and smaller near the edges of the spectrum - we quantitatively analyze the correlation between them. We elucidate the effect of (proximity to) integrability, showing how low-entanglement and low-PR states appear also in the middle of the spectrum as one approaches integrable points. We also determine the precise scaling behavior of the eigenstate-to-eigenstate fluctuations of the PR and EE with respect to system size, and characterize the statistical distribution of these quantities near the middle of the spectrum.
Many-Body Perturbation Theory Lucia Reining, Fabien Bruneval
Botti, Silvana
Many-Body Perturbation Theory Lucia Reining, Fabien Bruneval Laboratoire des Solides Irradi.6.2007 Many-Body Perturbation Theory Lucia Reining #12;Reminder PT EoM HF Screening Outline 1 Reminder 2 Perturbation Theory 3 Equation of Motion 4 Hartree Fock 5 Screened Equations Many-Body Perturbation Theory
Relativistic many-body XMCD theory including core degenerate effects
NASA Astrophysics Data System (ADS)
Fujikawa, Takashi
2009-11-01
A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2. In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.
Hong-Ou-Mandel Interference with Atomic Many-Body States
NASA Astrophysics Data System (ADS)
Islam, Rajibul; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Rispoli, Matthew; Tai, M. Eric; Greiner, Markus
2015-05-01
Hong-Ou-Mandel (HOM) interference experiments are a powerful probe for the indistinguishability and underlying quantum statistics of particles. In the classic HOM experiment, a pair of identical photons incident on different input ports of a beamsplitter exits via the same output port. Using the precise control and readout afforded by our quantum gas microscope, we present an implementation of this classic experiment using massive bosons in a doublewell optical potential. Identical states are prepared on each site of the doublewell and by lowering the tunnel coupling between the sites for specific times, we drive a beam splitter operation between the sites. For single-atom Fock input states, we have realized a high fidelity beamsplitter operation and observed an HOM interference contrast of >90%. By generalizing to more complex initial states on the input ports, we have been able to establish HOM experiment protocols as a robust approach towards studying the indistinguishability of many-body states as well as probe interaction-induced effects. These techniques open a path towards the measurement of purity in a quantum system and entanglement entropy in many-body states.
Local reversibility and entanglement structure of many-body ground states
Tomotaka Kuwahara; Itai Arad; Luigi Amico; Vlatko Vedral
2015-03-03
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are relevant both to critical and non-critical theories.
Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
The self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo J. Chem. Phys. {\\bf 136}, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. {\\bf 89}, 6316 (1988)] are blended to obtain a method for the calculation of thermodynamic properties of many-body systems at low temperatures. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric trial wave functions. A statistical method is derived for the calculation of finite temperature properties of many-body systems near the ground state. In the process we also obtain a parallel algorithm that optimizes the many-body basis of a small subspace of the many-body Hilbert space. This small subspace is optimized to have maximum overlap with the one expanded by the lower energy eigenstates of a many-body Hamiltonian. We show in a model system that the Helmholtz free energy is minimized within this subspace as the iteration number increases. We show that the subspace expanded by the small basis systematically converges towards the subspace expanded by the lowest energy eigenstates. Possible applications of this method to calculate the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can be also used to accelerate the calculation of the ground or excited states with Quantum Monte Carlo.
Many-body electronic structure of americium metal.
Savrasov, Sergej Y; Haule, Kristjan; Kotliar, Gabriel
2006-01-27
We report computer based simulations of energetics, spectroscopy, and electron-phonon interaction of americium using a novel spectral density functional method. This approach gives rise to a new concept of a many-body electronic structure and reveals the unexpected mixed valence regime of Am 5f6 electrons which under pressure acquire the 5f7 valence state. This explains the unique properties of Am and addresses the fundamental issue of how the localization delocalization edge is approached from the localized side in a closed shell system. PMID:16486744
Charge optimized many-body potential for aluminum
NASA Astrophysics Data System (ADS)
Choudhary, Kamal; Liang, Tao; Chernatynskiy, Aleksandr; Lu, Zizhe; Goyal, Anuj; Phillpot, Simon R.; Sinnott, Susan B.
2015-01-01
An interatomic potential for Al is developed within the third generation of the charge optimized many-body (COMB3) formalism. The database used for the parameterization of the potential consists of experimental data and the results of first-principles and quantum chemical calculations. The potential exhibits reasonable agreement with cohesive energy, lattice parameters, elastic constants, bulk and shear modulus, surface energies, stacking fault energies, point defect formation energies, and the phase order of metallic Al from experiments and density functional theory. In addition, the predicted phonon dispersion is in good agreement with the experimental data and first-principles calculations. Importantly for the prediction of the mechanical behavior, the unstable stacking fault energetics along the < {12\\bar{{1}}}> direction on the (1?1?1) plane are similar to those obtained from first-principles calculations. The polycrsytal when strained shows responses that are physical and the overall behavior is consistent with experimental observations.
Constructing local integrals of motion in the many-body localized phase
NASA Astrophysics Data System (ADS)
Chandran, Anushya; Kim, Isaac H.; Vidal, Guifre; Abanin, Dmitry A.
2015-02-01
Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body-localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin-flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, in both experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin-chain model. We show that the resulting LIOMs are quasilocal and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures. PMID:25144610
Improved variational many-body wave function in light nuclei
Usmani, Q. N.; Anwar, K.; Singh, A.; Rawitscher, G.
2009-09-15
We propose and implement a simple method for improving the variational wave function of a many-body system. We have obtained a significant improvement in the binding energies, wave functions, and variance for the light nuclei {sup 3}H, {sup 4}He, and {sup 6}Li, using the fully realistic Argonne (AV{sub 18}) two-body and Urbana-IX (UIX) three-body interactions. The energy of {sup 4}He was improved by about 0.2 MeV and the {sup 6}Li binding energy was increased by {approx_equal}1.7 MeV compared to earlier variational Monte Carlo results. The latter result demonstrates the significant progress achieved by our method, and detailed analyses of the improved results are given. With central interactions the results are found to be in agreement with the 'exact' calculations. Our study shows that the relative error in the many-body wave functions, compared to two-body pair correlations, increases rapidly at least proportionally to the number of pairs in the system. However, this error does not increase indefinitely since the pair interactions saturate owing to convergence of cluster expansion.
Photon-mediated interactions: a scalable tool to create and sustain entangled many-body states
Camille Aron; Manas Kulkarni; Hakan E. Türeci
2014-12-29
Generation and sustenance of entangled many-body states is of fundamental and applied interest. Recent experimental progress in the stabilization of two-qubit Bell states in superconducting quantum circuits using an autonomous feedback scheme [S. Shankar et al., Nature 504, 419 (2013)] has demonstrated the effectiveness and robustness of driven-dissipative approaches, i.e. engineering a fine balance between driven-unitary and dissipative dynamics. Despite the remarkable theoretical and experimental progress in those approaches for superconducting circuits, no demonstrably scalable scheme exists to drive an arbitrary number of spatially separated qubits to a desired entangled quantum many-body state. Here we propose and study such a scalable scheme, based on engineering photon-mediated interactions, for driving a register of spatially separated qubits into multipartite entangled states. We demonstrate how generalized W-states can be generated with remarkable fidelities and the entanglement sustained for an indefinite time. The protocol is primarily discussed for a superconducting circuit architecture but is ideally realized in any platform that permits controllable delivery of coherent light to specified locations in a network of Cavity QED systems.
No-go theorem for one-way quantum computing on naturally occurring two-level systems
Chen, Jianxin
The ground states of some many-body quantum systems can serve as resource states for the one-way quantum computing model, achieving the full power of quantum computation. Such resource states are found, for example, in ...
Cavity-Free Photon Blockade Induced by Many-Body Bound States
NASA Astrophysics Data System (ADS)
Zheng, Huaixiu; Gauthier, Daniel; Baranger, Harold
2012-02-01
We show theoretically that a variety of strong quantum nonlinear phenomena occur in a completely open one-dimensional waveguide coupled to an N-type four-level system. This system could be realized, for example, in experiments using superconducting circuits. We focus on photon blockade, photon-induced tunneling, bunching or anti-bunching, and the creation of single-photon states, all in the absence of a cavity. Many-body bound states appear due to the strong photon-photon correlation mediated by the four-level system. These bound states cause photon blockade, generating a sub-Poissonian single-photon source [1]. Such a source is crucial for quantum cryptography and distributed quantum networking; our work thus supports the notion that open quantum systems can play a critical role in the manipulation of individual, mobile quanta, a key goal of quantum communication. [1] H. Zheng, D. J. Gauthier, and H. U. Baranger, Phys. Rev. Lett. in press (2011), arXiv:1107.0309.
Many-body formalism for fermions: Enforcing the Pauli principle on paper
NASA Astrophysics Data System (ADS)
Watson, D. K.
2015-07-01
Confined quantum systems involving N identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with N and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.
Many-body localisation implies that eigenvectors are matrix-product states
M. Friesdorf; A. H. Werner; W. Brown; V. B. Scholz; J. Eisert
2014-11-18
The phenomenon of many-body localisation received a lot of attention recently, both for its implications in condensed-matter physics of allowing systems to be an insulator even at non-zero temperature as well as in the context of the foundations of quantum statistical mechanics, providing examples of systems showing the absence of thermalisation following out-of-equilibrium dynamics. In this work, we establish a novel link between dynamical properties - the absence of a group velocity and transport - with entanglement properties of individual eigenvectors. Using Lieb-Robinson bounds and filter functions, we prove rigorously under simple assumptions on the spectrum that if a system shows strong dynamical localisation, all of its many-body eigenvectors have clustering correlations. In one dimension this implies directly an entanglement area law, hence the eigenvectors can be approximated by matrix-product states. We also show this statement for parts of the spectrum, allowing for the existence of a mobility edge above which transport is possible.
Many-body wave scattering by small bodies and applications
A. G. Ramm
2007-07-20
A rigorous reduction of the many-body wave scattering problem to solving a linear algebraic system is given bypassing solving the usual system of integral equation. The limiting case of infinitely many small particles embedded into a medium is considered and the limiting equation for the field in the medium is derived. The impedance boundary conditions are imposed on the boundaries of small bodies. The case of Neumann boundary conditions (acoustically hard particles) is also considered. Applications to creating materials with a desired refraction coefficient are given. It is proved that by embedding suitable number of small particles per unit volume of the original material with suitable boundary impedances one can create a new material with any desired refraction coefficient. The governing equation is a scalar Helmholtz equation, which one obtains by Fourier transforming the wave equation.
Blood-Forsythe, Martin A; DiStasio, Robert A; Car, Roberto; Aspuru-Guzik, Alán
2015-01-01
Accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrossetti et al., J. Chem. Phys. 140, 18A508 (2014)], in which the correlation energy is modeled at short-range by a semi-local density functional and at long-range by a model system of coupled quantum harmonic oscillators. In this work, we develop analytical gradients of the MBD energy with respect to nuclear coordinates, including all implicit coordinate dependencies arising from the partitioning of the charge density into Hirshfeld effective volumes. To demonstrate the efficiency and accuracy of these MBD gradients for geometry optimizations of systems with intermolecular and intramolecular interactions, we optimized conformers of the be...
Quantum Friction: Cooling Quantum Systems with Unitary Time Evolution
Aurel Bulgac; Michael McNeil Forbes; Kenneth J. Roche; Gabriel Wlaz?owski
2013-05-29
We introduce a type of quantum dissipation -- local quantum friction -- by adding to the Hamiltonian a local potential that breaks time-reversal invariance so as to cool the system. Unlike the Kossakowski-Lindblad master equation, local quantum friction directly effects unitary evolution of the wavefunctions rather than the density matrix: it may thus be used to cool fermionic many-body systems with thousands of wavefunctions that must remain orthogonal. In addition to providing an efficient way to simulate quantum dissipation and non-equilibrium dynamics, local quantum friction coupled with adiabatic state preparation significantly speeds up many-body simulations, making the solution of the time-dependent Schr\\"odinger equation significantly simpler than the solution of its stationary counterpart.
Adiabatic quantum metrology with strongly correlated quantum optical systems
P. A. Ivanov; D. Porras
2013-05-24
We show that the quasi-adiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a small symmetry-breaking perturbation at the quantum phase transition, that leads to the collapse of the wavefunciton into one of two possible ground states. The scaling of the final state properties with the number of atoms and with the intensity of the symmetry breaking field, can be interpreted in terms of the precession time of an effective quantum metrological protocol. We show that our ideas can be tested with spin-phonon interactions in trapped ion setups. Our work points to a classification of quantum phase transitions in terms of the capability of many-body quantum systems for parameter estimation.
Quantum chaotic system as a model of decohering environment
Jayendra N. Bandyopadhyay
2009-04-24
As a model of decohering environment, we show that quantum chaotic system behave equivalently as many-body system. An approximate formula for the time evolution of the reduced density matrix of a system interacting with a quantum chaotic environment is derived. This theoretical formulation is substantiated by the numerical study of decoherence of two qubits interacting with a quantum chaotic environment modeled by a chaotic kicked top. Like the many-body model of environment, the quantum chaotic system is efficient decoherer, and it can generate entanglement between the two qubits which have no direct interaction.
Particle diagrams and embedded many-body random matrix theory.
Small, R A; Müller, S
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ? m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k = m,3 k = m,...,nk = m. PMID:25122235
Particle diagrams and embedded many-body random matrix theory
NASA Astrophysics Data System (ADS)
Small, R. A.; Müller, S.
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ?m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k=m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
NASA Astrophysics Data System (ADS)
Kwasigroch, M. P.; Cooper, N. R.
2014-08-01
We study theoretically the collective dynamics of rotational excitations of polar molecules loaded into an optical lattice in two dimensions. We explore the collective many-body phases that form following a microwave pulse. We show that, owing to the long-range interactions between molecules and energy conservation in this isolated system, the rotational excitations can form a Bose-Einstein condensate with long-range order, even for the natural (undressed) dipole interactions. This manifests itself as a divergent T2 coherence time of the rotational transition even in the presence of inhomogeneous broadening. The dynamical evolution of a dense gas of rotational excitations shows regimes of nonergodicity, characteristic of many-body localization and localization protected quantum order.
The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
J. K. Freericks; B. K. Nikolic; O. Frieder
2014-12-09
Generating big data pervades much of physics. But some problems, which we call extreme data problems, are too large to be treated within big data science. The nonequilibrium quantum many-body problem on a lattice is just such a problem, where the Hilbert space grows exponentially with system size and rapidly becomes too large to fit on any computer (and can be effectively thought of as an infinite-sized data set). Nevertheless, much progress has been made with computational methods on this problem, which serve as a paradigm for how one can approach and attack extreme data problems. In addition, viewing these physics problems from a computer-science perspective leads to new approaches that can be tried to solve them more accurately and for longer times. We review a number of these different ideas here.
Many-body Rabi oscillations of Rydberg excitation in small mesoscopic samples
J. Stanojevic; R. Côté
2008-01-15
We investigate the collective aspects of Rydberg excitation in ultracold mesoscopic systems. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitation are the many-body Rabi oscillations, spatial correlations between atoms as well as the fluctuations of the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schr\\"edinger equation.
Pichler, H.; Daley, A. J.; Zoller, P. [Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria) and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria)
2010-12-15
We analyze in detail the heating of bosonic atoms in an optical lattice due to incoherent scattering of light from the lasers forming the lattice. Because atoms scattered into higher bands do not thermalize on the time scale of typical experiments, this process cannot be described by the total energy increase in the system alone (which is determined by single-particle effects). The heating instead involves an important interplay between the atomic physics of the heating process and the many-body physics of the state. We characterize the effects on many-body states for various system parameters, where we observe important differences in the heating for strongly and weakly interacting regimes, as well as a strong dependence on the sign of the laser detuning from the excited atomic state. We compute heating rates and changes to characteristic correlation functions based on both perturbation-theory calculations and a time-dependent calculation of the dissipative many-body dynamics. The latter is made possible for one-dimensional systems by combining time-dependent density-matrix-renormalization-group methods with quantum trajectory techniques.
Understanding many-body physics in one dimension from the Lieb–Liniger model
NASA Astrophysics Data System (ADS)
Jiang, Yu-Zhu; Chen, Yang-Yang; Guan, Xi-Wen
2015-05-01
This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb–Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe’s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb–Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang–Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb–Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability. Project supported by the National Basic Research Program of China (Grant No. 2012CB922101) and the National Natural Science Foundation of China (Grant Nos. 11374331 and 11304357).
Communication: Random phase approximation renormalized many-body perturbation theory
Bates, Jefferson E.; Furche, Filipp
2013-11-07
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations.
Dynamics at the Many-Body Localization Transition
NASA Astrophysics Data System (ADS)
Santos, Lea; Torres-Herrera, Jonathan
2015-05-01
Studies about localization in interacting systems have recently boomed. The interest in the subject is motivated by indications of the existence of a many-body localization (MBL) phase and by advances in experiments with optical lattices, which may serve as testbeds for corroborating theoretical predictions. A paradigmatic system for these analysis is the one-dimensional isolated Heisenberg model with random magnetic fields. We study the dynamics of this system for initial states prepared with high energies. Our focus is on the probability for finding the initial state later in time, the so-called survival probability. Two distinct behaviors are identified before the saturation of the relaxation process. At short times, the decay is very fast, as typical of clean systems. It subsequently slows down and develops a powerlaw behavior with an exponent related with the multifractal structure of the eigenstates. The curve of the powerlaw exponent versus the disorder strength exhibits an inflection point that is associated with the metal-insulator transition point. This work was supported by the NSF grant No. DMR-1147430.
Tsatsos, Marios C.; Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S. [Theoretische Chemie, Physikalisch-Chemisches Institut, Universitaet Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg (Germany)
2010-09-15
A three-dimensional attractive Bose-Einstein condensate is expected to collapse when the number of the particles N in the ground state or the interaction strength {lambda}{sub 0} exceeds a critical value. We study systems of different particle numbers and interaction strength and find that even if the overall ground state is collapsed there is a plethora of fragmented excited states that are still in the metastable region. Utilizing the configuration interaction expansion we determine the spectrum of the ground (''yrast'') and excited many-body states with definite total angular-momentum quantum numbers 0{<=}L{<=}N and -L{<=}M{sub L{<=}}L, and we find and examine states that survive the collapse. This opens up the possibility of realizing a metastable system with overcritical numbers of bosons in a ground state with angular momentum L{ne}0. The multiorbital mean-field theory predictions about the existence of fragmented metastable states with overcritical numbers of bosons are verified and elucidated at the many-body level. The descriptions of the total angular momentum within the mean-field and the many-body approaches are compared.
Many-body theory of chemotactic cell-cell interactions.
Newman, T J; Grima, R
2004-11-01
We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling epsilon , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient D(R)--an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that D(R) is renormalized to zero at a critical value of epsilon, indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that D(R) approximately epsilon(-2) , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion. PMID:15600665
Many-body theory of positron annihilation on core electrons
NASA Astrophysics Data System (ADS)
Green, Dermot; Ludlow, John; Gribakin, Gleb
2014-05-01
Positron annihilation on core electrons is a key process for several experimental techniques. Interpretation of the measured annihilation spectra relies heavily on theoretical input. Specifically, one needs to know the relative probabilities of positron annihilation with inner electrons of various atoms. These are usually calculated using the independent particle model (IPM) with a phenomenological enhancement factor that attempts to account for the important effect of electron-positron correlations. We use diagrammatic many-body theory (MBT), developed by the authors, to calculate the individual contributions from each electronic subshell to the total ?-spectra and rate parameter Zeff for positron annihilation on the core electrons of the noble gases. We show that the enhancement of the annihilation rate and gamma-spectra due to short-range correlations is significant even for the tightly-bound core electrons, and that proper account of the core contribution must be taken to accurately describe experimental spectra. Furthermore, we use the ab initio theory to calculate enhancement factors that can be used in IPM calculations for annihilation on core electrons of atoms across the periodic table and on the atomic-like core electrons of condensed matter systems.
Particle Diagrams and Statistics of Many-Body Random Potentials
Rupert Small; Sebastian Müller
2014-12-09
We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the method of supersymmetry and the eigenvector expansion technique pioneered in [1]. We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with $m$ bosons or fermions that interact through a random $k$-body Hermitian potential ($k \\le m$); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble (eGUE) [2]. Our results apply in the limit where the number $l$ of available single-particle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semi-circular level density for $m nk$ for the $2n$-th moment.
Many-body theory of chemotactic cell-cell interactions
NASA Astrophysics Data System (ADS)
Newman, T. J.; Grima, R.
2004-11-01
We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling ? , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient DR —an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that DR is renormalized to zero at a critical value of ? , indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that DR˜?-2 , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion.
Experimental signatures of semiclassical gravity and the many-body Schrodinger-Newton equation
NASA Astrophysics Data System (ADS)
Helou, Bassam
2015-04-01
In semiclassical gravity, the many-body Schrodinger-Newton (SN) equation, which governs the evolution of a many-particle system under self gravity, predicts that classical and quantum eigenfrequencies of a macroscopic mechanical oscillator are different. For high- Q and low-frequency (~ 10s of mHz) torsional pendulums made with atoms with small internal motion fluctuations, such as Tungsten or Platinum, this difference can be considerably larger than the classical eigenfrequency of the pendulum. We exploit this split in the design of an optomechanics experiment which, in contrast with experiments that test for quantum gravity, is feasible with current technology and which distinguishes, at low temperatures and within about a year, between the predictions of the SN equation and standard quantum mechanics. Specifically, we propose using light to probe the motion of such oscillators. Moreover, the nonlinearity induced by the SN equation forces us to revisit the wavefunction collapse postulate, resulting in two proposed prescriptions for how the measurement of the light is performed. Each predict a noticeable feature in the spectrum of the outgoing light that is separate from the features of classical force noise.
Experimental signatures of semiclassical gravity and the many-body Schrödinger-Newton equation
NASA Astrophysics Data System (ADS)
Helou, Bassam; Miao, Haixing; Yang, Huan; Chen, Yanbei
2015-04-01
In semiclassical gravity, the many-body Schrödinger-Newton (SN) equation, which governs the evolution of a many-particle system under self gravity, predicts that classical and quantum eigenfrequencies of a macroscopic mechanical oscillator are different. For high- Q and low-frequency (~10s of mHz) torsional pendulums made with atoms with small internal motion fluctuations, such as Tungsten or Platinum, this difference can be considerably larger than the classical eigenfrequency of the pendulum. We exploit this split in the design of an optomechanics experiment which, in contrast with experiments that test for quantum gravity, is feasible with current technology and which distinguishes, at low temperatures and within about a year, between the predictions of the SN equation and standard quantum mechanics. Specifically, we propose using light to probe the motion of such oscillators. Moreover, the nonlinearity induced by the SN equation forces us to revisit the wavefunction collapse postulate, resulting in two proposed prescriptions for how the measurement of the light is performed. Each predict a noticeable feature in the spectrum of the outgoing light that is separate from the features of classical force noise.
On the representation of many-body interactions in water
NASA Astrophysics Data System (ADS)
Medders, Gregory R.; Götz, Andreas W.; Morales, Miguel A.; Bajaj, Pushp; Paesani, Francesco
2015-09-01
Recent work has shown that the many-body expansion of the interaction energy can be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and long-range interactions at different orders is investigated by analyzing water potentials that treat the leading terms of the many-body expansion through implicit (i.e., TTM3-F and TTM4-F PESs) and explicit (i.e., WHBB and MB-pol PESs) representations. It is found that explicit short-range representations of 2-body and 3-body interactions along with a physically correct incorporation of short- and long-range contributions are necessary for an accurate representation of the water interactions from the gas to the condensed phase. Similarly, a complete many-body representation of the dipole moment surface is found to be crucial to reproducing the correct intensities of the infrared spectrum of liquid water.
Observing CP Violation in Many-Body Decays
Mike Williams
2011-05-26
It is well known that observing CP violation in many-body decays could provide strong evidence for physics beyond the Standard Model. Many searches have been carried out; however, no 5sigma evidence for CP violation has yet been found in these types of decays. A novel model-independent method for observing CP violation in many-body decays is presented in this paper. It is shown that the sensitivity of this method is significantly larger than those used to-date.
Whither many-body theory. A summary of the Oulu Conference
NASA Astrophysics Data System (ADS)
Clark, J. W.
There are basically two types of contributions to many-body theory, those focusing on the development of new methods and techniques and those which seek to understand many-body phenomena in particular systems. The work presented at this conference is weighted far more heavily toward applications and toward the explication of mechanisms underlying observed phenomena than was the case at previous conferences. In the topical composition of this conference we observe also a shift away from the hard-core systems (the helium liquids and solids, nuclei, nuclear matter) which have dominated the attention of microscopic theorists for three decades. The new emphasis is on not-so-strongly-interacting systems, primarily electronic systems in various guises of current experimental relevance. In particular, the impact of the new discoveries of high-temperature superconductors on the thrust of many-body theories is already apparent in many of the papers at this conference.
Reboredo, Fernando A.; Kim, Jeongnim
2014-02-21
A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.
Many-Body Localization Characterized from a One-Particle Perspective
NASA Astrophysics Data System (ADS)
Bera, Soumya; Schomerus, Henning; Heidrich-Meisner, Fabian; Bardarson, Jens H.
2015-07-01
We show that the one-particle density matrix ? can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ? ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ? ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.
Many-Body Localization Characterized from a One-Particle Perspective.
Bera, Soumya; Schomerus, Henning; Heidrich-Meisner, Fabian; Bardarson, Jens H
2015-07-24
We show that the one-particle density matrix ? can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ?) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ?) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase. PMID:26252702
Many-Body Effects on Bandgap Shrinkage, Effective Masses, and Alpha Factor
NASA Technical Reports Server (NTRS)
Li, Jian-Zhong; Ning, C. Z.; Woo, Alex C. (Technical Monitor)
2000-01-01
Many-body Coulomb effects influence the operation of quantum-well (QW) laser diode (LD) strongly. In the present work, we study a two-band electron-hole plasma (EHP) within the Hatree-Fock approximation and the single plasmon pole approximation for static screening. Full inclusion of momentum dependence in the many-body effects is considered. An empirical expression for carrier density dependence of the bandgap renormalization (BGR) in an 8 nm GaAs/Al(0.3)G(4.7)As single QW will be given, which demonstrates a non-universal scaling behavior for quasi-two-dimension structures, due to size-dependent efficiency of screening. In addition, effective mass renormalization (EMR) due to momentum-dependent self-energy many-body correction, for both electrons and holes is studied and serves as another manifestation of the many-body effects. Finally, the effects on carrier density dependence of the alpha factor is evaluated to assess the sensitivity of the full inclusion of momentum dependence.
Many-body mobility edge due to symmetry-constrained dynamics and strong interactions
NASA Astrophysics Data System (ADS)
Mondragon-Shem, Ian; Pal, Arijeet; Hughes, Taylor L.; Laumann, Chris R.
2015-08-01
We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-1 /2 XXZ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and antiferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.
Many-body interactions in quasi-freestanding graphene
Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei; Louie, Steven; Lanzara, Alessandra
2011-06-03
The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.
Many-body effects in two-dimensional Ostwald ripening
Hisao Hayakawa; Fereydoon Family
1990-01-01
A theory for Ostwald ripening in two dimensions is presented. Using a many-body approach, we show the existence of a screening length which had been previously assumed by Marqusee (J. Chem. Phys. 81 (1984) 976) in two-dimensional diffusion-controlled growth processes. We also confirm that the growth law of the critical droplet radius in our model is given by Rc(t)~t1\\/3. Present
Many-body interactions and melting of colloidal crystals
J. Dobnikar; Y. Chen; R. Rzehak; H. H. von Grünberg
2008-01-25
We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids. Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pair-interaction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions.
Effective separability of typical entangled many-body states
S. Camalet
2009-07-02
We consider two systems of harmonically trapped particles in a typical pure state of the Hilbert space defined by given values of the particle numbers and energies of the two gases. Such a state is entangled but we show that, for large systems, the resulting correlations between the two gases are identical to those of a separable mixture. This result can be generalized to other physical systems. We discuss the relation of this effective separability to the well-known existence of quantum correlations in any entangled state. We study in detail a small bipartite system and find that its correlations are well explained by the large systems results.
Center-of-mass corrections reexamined: A many-body expansion approach Bogdan Mihaila*
Mihaila, Bogdan
Center-of-mass corrections reexamined: A many-body expansion approach Bogdan Mihaila* Department-body expansion for the computation of the charge form factor in the center-of-mass system is proposed assumes a nuclear wave function that factorizes into a nuclear center-of-mass wave function, which
Dynamical many-body phases of the parametrically driven, dissipative Dicke model
NASA Astrophysics Data System (ADS)
Chitra, R.; Zilberberg, O.
2015-08-01
Control and manipulation of quantum engineered systems allows for the utilization of time-dependent parametric modulations for accessing novel out-of-equilibrium phenomena. In the absence of such driving, the dissipative Dicke model exhibits a fascinating out-of-equilibrium many-body phase transition as a function of a coupling between a driven photonic cavity and numerous two-level atoms. We study the effect of a parametric modulation of this coupling and discover a rich phase diagram as a function of the modulation strength. We find that in addition to the established normal and super-radiant phases, a new phase with pulsed superradiance, which we term dynamical normal phase, appears when the system is parametrically driven. Employing different methods, we characterize the different phases and the transitions between them. Specific heed is paid to the role of dissipation in determining the phase boundaries. Our analysis paves the road for the experimental study of dynamically stabilized phases of interacting light and matter.
Uncovering many-body correlations in nanoscale nuclear spin baths by central spin decoherence
Wen-Long Ma; Gary Wolfowicz; Nan Zhao; Shu-Shen Li; John J. L. Morton; Ren-Bao Liu
2014-04-10
Many-body correlations can yield key insights into the nature of interacting systems; however, detecting them is often very challenging in many-particle physics, especially in nanoscale systems. Here, taking a phosphorus donor electron spin in a natural-abundance 29Si nuclear spin bath as our model system, we discover both theoretically and experimentally that many-body correlations in nanoscale nuclear spin baths produce identifiable signatures in the decoherence of the central spin under multiple-pulse dynamical decoupling control. We find that when the number of decoupling -pulses is odd, central spin decoherence is primarily driven by second-order nuclear spin correlations (pairwise flip-flop processes). In contrast, when the number of -pulses is even, fourth-order nuclear spin correlations (diagonal interaction renormalized pairwise flip-flop processes) are principally responsible for the central spin decoherence. Many-body correlations of different orders can thus be selectively detected by central spin decoherence under different dynamical decoupling controls, providing a useful approach to probing many-body processes in nanoscale nuclear spin baths.
Many-body-theory study of lithium photoionization
NASA Technical Reports Server (NTRS)
Chang, T. N.; Poe, R. T.
1975-01-01
A detailed theoretical calculation is carried out for the photoionization of lithium at low energies within the framework of Brueckner-Goldstone perturbational approach. In this calculation extensive use is made of the recently developed multiple-basis-set technique. Through this technique all second-order perturbation terms, plus a number of important classes of terms to infinite order, have been taken into account. Analysis of the results enables one to resolve the discrepancies between two previous works on this subject. The detailed calculation also serves as a test on the convergence of the many-body perturbation-expansion approach.
Collective Many-Body Interaction in Rydberg Dressed Atoms
Honer, Jens; Weimer, Hendrik; Buechler, Hans Peter; Pfau, Tilman
2010-10-15
We present a method to control the shape and character of the interaction potential between cold atomic gases by weakly dressing the atomic ground state with a Rydberg level. For increasing particle densities, a crossover takes place from a two-particle interaction into a collective many-body interaction, where the dipole-dipole or van der Waals blockade phenomenon between the Rydberg levels plays a dominant role. We study the influence of these collective interaction potentials on a Bose-Einstein condensate and present the optimal parameters for its experimental detection.
Three-body decay of many-body resonances
Jensen, A.S.; Fedorov, D.V.; Fynbo, H.O.U. [Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C (Denmark); Garrido, E. [Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain)
2005-10-14
We use the hyperspherical coordinates to describe decay of many-body resonances. Direct and sequential decay are described by different paths in the distances between the particles. We generalize the WKB expression for the {alpha}-decay width to decay of three charged particles. Decay mechanisms and resonance structures are computed in coordinate space. The energy distributions of the particles after decay are discussed. Moderate s-wave scattering lengths prefer decay via corresponding virtual state possibly leaving unique fingerprints of this reminiscence of the Efimov effect in the decay of excited states. Numerical illustrations are resonances in 6He, 12C, 17Ne.
Krishtal, Alisa; Genova, Alessandro; Pavanello, Michele
2015-01-01
Subsystem Density-Functional Theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to the computation of condensed phase systems, their excited states, and the evaluation of many-body interactions between the subsystems. As subsystem DFT is in principle an exact theory, any advance in this field can have a dual role. One is the possible applicability of a resulting method in practical calculations. The other is the possibility of shedding light on some quantum-mechanical phenomenon which is more easily treated by subdividing a supersystem into subsystems. An example of the latter is many-body interactions. In the discussion, we present some recent work from our research group as well as some new results, casting them in the current state-of-the-art in this review as comprehensively as possible.
Many-body dispersion effects in the binding of adsorbates on metal surfaces
NASA Astrophysics Data System (ADS)
Maurer, Reinhard J.; Ruiz, Victor G.; Tkatchenko, Alexandre
2015-09-01
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic-inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate-surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches.
Topological and nematic ordered phases in many-body cluster-Ising models
NASA Astrophysics Data System (ADS)
Giampaolo, S. M.; Hiesmayr, B. C.
2015-07-01
We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size n +2 and is reached exactly when both interactions are equally weighted. For even n we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd n to a symmetry-protected topological ordered phase. Though complex, we are able to quantify the multiparticle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no n +1 -partite entanglement. This is possible since the nontrivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough (local) genuine n +2 -partite entanglement is built up. Due to their analytical solvableness the n -cluster-Ising models serve as a prototype for studying nontrivial-spin orderings, and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.
Many-body dispersion effects in the binding of adsorbates on metal surfaces.
Maurer, Reinhard J; Ruiz, Victor G; Tkatchenko, Alexandre
2015-09-14
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic-inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate-surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches. PMID:26374001
Many-Body Dispersion Effects in the Binding of Adsorbates on Metal Surfaces
Maurer, Reinhard J; Tkatchenko, Alexandre
2015-01-01
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic--inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Phys. Rev. Lett. 108, 236402 (2012); J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid (PTCDA), and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects we are abl...
Topological and nematic ordered phases in many-body cluster-Ising models
S. M. Giampaolo; B. C. Hiesmayr
2015-06-23
We present a fully analytically solvable family of models with many-body cluster interaction and Ising interaction. This family exhibits two phases, dubbed cluster and Ising phases, respectively. The critical point turns out to be independent of the cluster size $n+2$ and is reached exactly when both interactions are equally weighted. For even $n$ we prove that the cluster phase corresponds to a nematic ordered phase and in the case of odd $n$ to a symmetry protected topological ordered phase. Though complex, we are able to quantify the multi-particle entanglement content of neighboring spins. We prove that there exists no bipartite or, in more detail, no $n+1$-partite entanglement. This is possible since the non-trivial symmetries of the Hamiltonian restrict the state space. Indeed, only if the Ising interaction is strong enough (local) genuine $n+2$-partite entanglement is built up. Due to their analytically solvableness the $n$-cluster-Ising models serve as a prototype for studying non trivial-spin orderings and due to their peculiar entanglement properties they serve as a potential reference system for the performance of quantum information tasks.
First-principles energetics of water clusters and ice: A many-body analysis
NASA Astrophysics Data System (ADS)
Gillan, M. J.; Alfè, D.; Bartók, A. P.; Csányi, G.
2013-12-01
Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
First-principles energetics of water clusters and ice: A many-body analysis
Gillan, M. J.; Alfè, D.; Thomas Young Centre, UCL, London WC1H 0AH; Department of Physics and Astronomy, UCL, London WC1E 6BT; Department of Earth Sciences, UCL, London WC1E 6BT ; Bartók, A. P.; Csányi, G.
2013-12-28
Standard forms of density-functional theory (DFT) have good predictive power for many materials, but are not yet fully satisfactory for cluster, solid, and liquid forms of water. Recent work has stressed the importance of DFT errors in describing dispersion, but we note that errors in other parts of the energy may also contribute. We obtain information about the nature of DFT errors by using a many-body separation of the total energy into its 1-body, 2-body, and beyond-2-body components to analyze the deficiencies of the popular PBE and BLYP approximations for the energetics of water clusters and ice structures. The errors of these approximations are computed by using accurate benchmark energies from the coupled-cluster technique of molecular quantum chemistry and from quantum Monte Carlo calculations. The systems studied are isomers of the water hexamer cluster, the crystal structures Ih, II, XV, and VIII of ice, and two clusters extracted from ice VIII. For the binding energies of these systems, we use the machine-learning technique of Gaussian Approximation Potentials to correct successively for 1-body and 2-body errors of the DFT approximations. We find that even after correction for these errors, substantial beyond-2-body errors remain. The characteristics of the 2-body and beyond-2-body errors of PBE are completely different from those of BLYP, but the errors of both approximations disfavor the close approach of non-hydrogen-bonded monomers. We note the possible relevance of our findings to the understanding of liquid water.
Many-body effects on adiabatic passage through Feshbach resonances
Tikhonenkov, I.; Pazy, E.; Band, Y. B.; Vardi, A.; Fleischhauer, M.
2006-04-15
We theoretically study the dynamics of an adiabatic sweep through a Feshbach resonance, thereby converting a degenerate quantum gas of fermionic atoms into a degenerate quantum gas of bosonic dimers. Our analysis relies on a zero temperature mean-field theory which accurately accounts for initial molecular quantum fluctuations, triggering the association process. The structure of the resulting semiclassical phase space is investigated, highlighting the dynamical instability of the system towards association, for sufficiently small detuning from resonance. It is shown that this instability significantly modifies the finite-rate efficiency of the sweep, transforming the single-pair exponential Landau-Zener behavior of the remnant fraction of atoms {gamma} on sweep rate {alpha}, into a power-law dependence as the number of atoms increases. The obtained nonadiabaticity is determined from the interplay of characteristic time scales for the motion of adiabatic eigenstates and for fast periodic motion around them. Critical slowing-down of these precessions near the instability leads to the power-law dependence. A linear power law {gamma}{proportional_to}{alpha} is obtained when the initial molecular fraction is smaller than the 1/N quantum fluctuations, and a cubic-root power law {gamma}{proportional_to}{alpha}{sup 1/3} is attained when it is larger. Our mean-field analysis is confirmed by exact calculations, using Fock-space expansions. Finally, we fit experimental low temperature Feshbach sweep data with a power-law dependence. While the agreement with the experimental data is well within experimental error bars, similar accuracy can be obtained with an exponential fit, making additional data highly desirable.
Approaching the complete-basis limit with a truncated many-body expansion.
Richard, Ryan M; Lao, Ka Un; Herbert, John M
2013-12-14
High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-? basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion-water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers. PMID:24329051
Approaching the complete-basis limit with a truncated many-body expansion
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2013-12-14
High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-? basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion–water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers.
Approaching the complete-basis limit with a truncated many-body expansion
NASA Astrophysics Data System (ADS)
Richard, Ryan M.; Lao, Ka Un; Herbert, John M.
2013-12-01
High-accuracy electronic structure calculations with correlated wave functions demand the use of large basis sets and complete-basis extrapolation, but the accuracy of fragment-based quantum chemistry methods has most often been evaluated using double-? basis sets, with errors evaluated relative to a supersystem calculation using the same basis set. Here, we examine the convergence towards the basis-set limit of two- and three-body expansions of the energy, for water clusters and ion-water clusters, focusing on calculations at the level of second-order Møller-Plesset perturbation theory (MP2). Several different corrections for basis-set superposition error (BSSE), each consistent with a truncated many-body expansion, are examined as well. We present a careful analysis of how the interplay of errors (from all sources) influences the accuracy of the results. We conclude that fragment-based methods often benefit from error cancellation wherein BSSE offsets both incompleteness of the basis set as well as higher-order many-body effects that are neglected in a truncated many-body expansion. An n-body counterpoise correction facilitates smooth extrapolation to the MP2 basis-set limit, and at n = 3 affords accurate results while requiring calculations in subsystems no larger than trimers.
Relaxation of isolated quantum systems beyond chaos.
García-Mata, Ignacio; Roncaglia, Augusto J; Wisniacki, Diego A
2015-01-01
In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is--to say the least--fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many-body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system. PMID:25679559
Relaxation of isolated quantum systems beyond chaos
NASA Astrophysics Data System (ADS)
García-Mata, Ignacio; Roncaglia, Augusto J.; Wisniacki, Diego A.
2015-01-01
In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is—to say the least—fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many-body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system.
Many-body tight-binding model for aluminum nanoparticles
Staszewska, Grazyna; Staszewski, Przemyslaw; Schultz, Nathan E.; Truhlar, Donald G. [Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5, 87-100 Torun (Poland); Department of Theoretical Foundations of Biomedical Sciences and Medical Informatics, Collegium Medicum, Nicolaus Copernicus University, ul. Jagiellonska 13, 85-067 Bydgoszcz (Poland); Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 44455-0431 (United States)
2005-01-15
A new, parametrized many-body tight-binding model is proposed for calculating the potential energy surface for aluminum nanoparticles. The parameters have been fitted to reproduce the energies for a variety of aluminum clusters (Al{sub 2}, Al{sub 3}, Al{sub 4}, Al{sub 7}, Al{sub 13}) calculated recently by the PBE0/MG3 method as well as the experimental face-centered-cubic cohesive energy, lattice constant, and a small set of Al cluster ionization potentials. Several types of parametrization are presented and compared. The mean unsigned error per atom for the best model is less than 0.03 eV.
Effective Operators from Exact Many-Body Renormalization
Lisetskiy, A F; Kruse, M G; Barrett, B R; Navratil, P; Stetcu, I; Vary, J P
2009-06-11
We construct effective two-body Hamiltonians and E2 operators for the p-shell by performing 16{h_bar}{Omega} ab initio no-core shell model (NCSM) calculations for A = 5 and A = 6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the 0{h_bar}{Omega} space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei.
Electric dipole polarizability: from few- to many-body systems
Miorelli, Mirko; Barnea, Nir; Hagen, Gaute; Orlandini, Giuseppina; Papenbrock, Thomas
2015-01-01
We review the Lorentz integral transform coupled-cluster method for the calculation of the electric dipole polarizability. We benchmark our results with exact hyperspherical harmonics calculations for 4He and then we move to a heavier nucleus studying 16O. We observe that the implemented chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order underestimates the electric dipole polarizability.
Electric dipole polarizability: from few- to many-body systems
Mirko Miorelli; Sonia Bacca; Nir Barnea; Gaute Hagen; Giuseppina Orlandini; Thomas Papenbrock
2015-09-01
We review the Lorentz integral transform coupled-cluster method for the calculation of the electric dipole polarizability. We benchmark our results with exact hyperspherical harmonics calculations for 4He and then we move to a heavier nucleus studying 16O. We observe that the implemented chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order underestimates the electric dipole polarizability.
NASA Astrophysics Data System (ADS)
McKinney, Brett; Dunn, Martin; Watson, Deborah
2002-05-01
Using many-body dimensional perturbation theory, we calculate the ground-state energy of a system of N trapped bosons interacting via hard-core repulsion. The atoms, as represented in the zeroth-order of our perturbation theory, are frozen in an equilibrium configuration, which is the symmetric minimum of an effective potential. In the first-order picture, the condensate atoms undergo normal mode oscillations about this equilibrium configuration. Correlation effects are automatically included at zeroth order since all terms in the Hamiltonian are retained, at least approximately. The energy we obtain through harmonic- (first-) order is parameterized by the number of atoms N, making it straightforward to study condensates containing any number of atoms. We compare our ground-state energy predictions with the Gross-Pitaevskii equation (mean-field theory) and the modified Gross-Pitaevskii equation, which includes quantum corrections beyond the mean-field equation.
Many-body localization and delocalization in the two-dimensional continuum
NASA Astrophysics Data System (ADS)
Nandkishore, Rahul
2014-11-01
We discuss whether localization in the two-dimensional continuum can be stable in the presence of short-range interactions. We conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature T
Quantum statistics of interacting dimer spin systems.
Rüegg, Ch; Normand, B; Matsumoto, M; Niedermayer, Ch; Furrer, A; Krämer, K W; Güdel, H-U; Bourges, Ph; Sidis, Y; Mutka, H
2005-12-31
The compound TlCuCl(3) represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Würtz [Phys. Rev. B 50, 13 515 (1994)10.1103/Phys. Rev. B 50, 13515] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important. PMID:16486391
Quantum Statistics of Interacting Dimer Spin Systems
NASA Astrophysics Data System (ADS)
Rüegg, Ch.; Normand, B.; Matsumoto, M.; Niedermayer, Ch.; Furrer, A.; Krämer, K. W.; Güdel, H.-U.; Bourges, Ph.; Sidis, Y.; Mutka, H.
2005-12-01
The compound TlCuCl3 represents a model system of dimerized quantum spins with strong interdimer interactions. We investigate the triplet dispersion as a function of temperature by inelastic neutron scattering experiments on single crystals. By comparison with a number of theoretical approaches we demonstrate that the description of Troyer, Tsunetsugu, and Würtz [Phys. Rev. BPRBMDO0163-1829 50, 13 515 (1994)10.1103/PhysRevB.50.13515] provides an appropriate quantum statistical model for dimer spin systems at finite temperatures, where many-body correlations become particularly important.
Simulations of dipolar fluids using effective many-body isotropic interactions
NASA Astrophysics Data System (ADS)
Sindt, Julien O.; Camp, Philip J.
2015-07-01
The partition function of a system with pairwise-additive anisotropic dipole-dipole interactions is equal to that of a hypothetical system with many-body isotropic interactions [G. Stell, Phys. Rev. Lett. 32, 286 (1974)]. The effective many-body interactions contain n-body contributions of all orders. Each contribution is known as an expansion in terms of the particle-particle distances r, and the coefficients are temperature dependent. The leading-order two-body term is the familiar -r-6 attraction, and the leading-order three-body term is equivalent to the Axilrod-Teller interaction. In this work, a fluid of particles with the leading-order two-body and three-body interactions is compared to an equivalent dipolar soft-sphere fluid. Molecular simulations are used to determine the conditions under which the effective many-body interactions reproduce the fluid-phase structures of the dipolar system. The effective many-body interaction works well at moderately high temperatures but fails at low temperatures where particle chaining is expected to occur. It is shown that an adjustment of the coefficients of the two-body and three-body terms leads to a good description of the structure of the dipolar fluid even in the chaining regime, due primarily to the ground-state linear configuration of the three-body Axilrod-Teller interaction. The vapor-liquid phase diagrams of systems with different Axilrod-Teller contributions are determined. As the strength of the three-body interaction is increased, the critical temperature and density both decrease and disappear completely above a threshold strength, where chaining eventually suppresses the condensation transition.
Simulations of dipolar fluids using effective many-body isotropic interactions.
Sindt, Julien O; Camp, Philip J
2015-07-14
The partition function of a system with pairwise-additive anisotropic dipole-dipole interactions is equal to that of a hypothetical system with many-body isotropic interactions [G. Stell, Phys. Rev. Lett. 32, 286 (1974)]. The effective many-body interactions contain n-body contributions of all orders. Each contribution is known as an expansion in terms of the particle-particle distances r, and the coefficients are temperature dependent. The leading-order two-body term is the familiar -r(-6) attraction, and the leading-order three-body term is equivalent to the Axilrod-Teller interaction. In this work, a fluid of particles with the leading-order two-body and three-body interactions is compared to an equivalent dipolar soft-sphere fluid. Molecular simulations are used to determine the conditions under which the effective many-body interactions reproduce the fluid-phase structures of the dipolar system. The effective many-body interaction works well at moderately high temperatures but fails at low temperatures where particle chaining is expected to occur. It is shown that an adjustment of the coefficients of the two-body and three-body terms leads to a good description of the structure of the dipolar fluid even in the chaining regime, due primarily to the ground-state linear configuration of the three-body Axilrod-Teller interaction. The vapor-liquid phase diagrams of systems with different Axilrod-Teller contributions are determined. As the strength of the three-body interaction is increased, the critical temperature and density both decrease and disappear completely above a threshold strength, where chaining eventually suppresses the condensation transition. PMID:26178112
Visualizing electronic correlations in molecules: STM images from many-body ab-initio calculations
Stefano Corni; Dimitrios Toroz; Massimo Rontani
2010-01-01
Single molecular orbitals are nowadays imaged in real space by both scanning tunnelling (STM) and photoemission spectroscopies. The key quantity provided by these techniques is the density of states --an intrinsically many-body observable. For extended systems, its energy and momentum dependence signals intriguing phenomena like non-Fermi liquid behavior, electron pairing, Kondo effect, Fermi edge singularity. For isolated molecules, the space-resolved
Encoding the structure of many-body localization with matrix product operators
NASA Astrophysics Data System (ADS)
Pekker, David; Clark, Bryan K.
2015-03-01
Anderson insulators are non-interacting disordered systems which have localized single particle eigenstates. The interacting analogue of Anderson insulators are the Many-Body Localized (MBL) phases. The natural language for representing the spectrum of the Anderson insulator is that of product states over the single-particle modes. We show that product states over Matrix Product Operators of small bond dimension is the corresponding natural language for describing the MBL phases. In this language all of the many-body eigenstates are encode by Matrix Product States (i.e. DMRG wave function) consisting of only two sets of low bond-dimension matrices per site: the Gi matrix corresponding to the local ground state on site i and the Ei matrix corresponding to the local excited state. All 2 n eigenstates can be generated from all possible combinations of these matrices.
Many-Body Spin Interactions and the Ground State of a Dense Rydberg Lattice Gas
Lesanovsky, Igor [Midlands Ultracold Atom Research Centre (MUARC), School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
2011-01-14
We study a one-dimensional atomic lattice gas in which Rydberg atoms are excited by a laser and whose external dynamics is frozen. We identify a parameter regime in which the Hamiltonian is well approximated by a spin Hamiltonian with quasilocal many-body interactions which possesses an exact analytic ground state solution. This state is a superposition of all states of the system that are compatible with an interaction induced constraint weighted by a fugacity. We perform a detailed analysis of this state which exhibits a crossover between a paramagnetic phase with short-ranged correlations and a crystal. This study also leads us to a class of spin models with many-body interactions that permit an analytic ground state solution.
Flow equation approach to one-body and many-body localization
NASA Astrophysics Data System (ADS)
Quito, Victor; Bhattacharjee, Paraj; Pekker, David; Refael, Gil
2014-03-01
We study one-body and many-body localization using the flow equation technique applied to spin-1/2 Hamiltonians. This technique, first introduced by Wegner, allows us to exact diagonalize interacting systems by solving a set of first-order differential equations for coupling constants. Besides, by the flow of individual operators we also compute physical properties, such as correlation and localization lengths, by looking at the flow of probability distributions of couplings in the Hilbert space. As a first example, we analyze the one-body localization problem written in terms of spins, the disordered XY model with a random transverse field. We compare the results obtained in the flow equation approach with the diagonalization in the fermionic language. For the many-body problem, we investigate the physical properties of the disordered XXZ Hamiltonian with a random transverse field in the z-direction.
Recent development of complex scaling method for many-body resonances and continua in light nuclei
Takayuki Myo; Yuma Kikuchi; Hiroshi Masui; Kiyoshi Kato
2014-10-16
The complex scaling method (CSM) is a useful similarity transformation of the Schr\\"odinger equation, in which bound-state spectra are not changed but continuum spectra are separated into resonant and non-resonant continuum ones. Because the asymptotic wave functions of the separated resonant states are regularized by the CSM, many-body resonances can be obtained by solving an eigenvalue problem with the $L^2$ basis functions. Applying this method to a system consisting of a core and valence nucleons, we investigate many-body resonant states in weakly bound nuclei very far from the stability lines. Non-resonant continuum states are also obtained with the discretized eigenvalues on the rotated branch cuts. Using these complex eigenvalues and eigenstates in CSM, we construct the extended completeness relations and Green's functions to calculate strength functions and breakup cross sections. Various kinds of theoretical calculations and comparisons with experimental data are presented.
A many-body potential approach to modelling the thermomechanical properties of actinide oxides.
Cooper, M W D; Rushton, M J D; Grimes, R W
2014-03-12
A many-body potential model for the description of actinide oxide systems, which is robust at high temperatures, is reported for the first time. The embedded atom method is used to describe many-body interactions ensuring good reproduction of a range of thermophysical properties (lattice parameter, bulk modulus, enthalpy and specific heat) between 300 and 3000 K for AmO2, CeO2, CmO2, NpO2, ThO2, PuO2 and UO2. Additionally, the model predicts a melting point for UO2 between 3000 and 3100 K, in close agreement with experiment. Oxygen-oxygen interactions are fixed across the actinide oxide series because it facilitates the modelling of oxide solid solutions. The new potential is also used to predict the energies of Schottky and Frenkel pair disorder processes. PMID:24553129
Many-body forces, isospin asymmetry and dense hyperonic matter
R. O. Gomes; V. Dexheimer; S. Schramm; C. A. Z. Vascconcellos
2015-04-10
The equation of state (EoS) of asymmetric nuclear matter at high densities is a key topic for the description of matter inside neutron stars. The determination of the properties of asymmetric nuclear matter, such as the symmetry energy ($a_{sym}$) and the slope of the symmetry energy ($L_0$) at saturation density, has been exaustively studied in order to better constrain the nuclear matter EoS. However, differently from symmetric matter properties that are reasonably constrained, the symmetry energy and its slope still large uncertainties in their experimental values. Regarding this subject, some studies point towards small values of the slope of the symmetry energy, while others suggest rather higher values. Such a lack of agreement raised a certain debate in the scientific community. In this paper, we aim to analyse the role of these properties on the behavior of asymmetric hyperonic matter. Using the formalism presented in Ref. (R.O. Gomes et al 2014}, which considers many-body forces contributions in the meson-baryon coupling, we calculate the EoS of asymmetric hyperonic matter and apply it to describe hyperonic matter and hyperon stars.
Many-body forces, isospin asymmetry and dense hyperonic matter
Gomes, R O; Schramm, S; Vascconcellos, C A Z
2015-01-01
The equation of state (EoS) of asymmetric nuclear matter at high densities is a key topic for the description of matter inside neutron stars. The determination of the properties of asymmetric nuclear matter, such as the symmetry energy ($a_{sym}$) and the slope of the symmetry energy ($L_0$) at saturation density, has been exaustively studied in order to better constrain the nuclear matter EoS. However, differently from symmetric matter properties that are reasonably constrained, the symmetry energy and its slope still large uncertainties in their experimental values. Regarding this subject, some studies point towards small values of the slope of the symmetry energy, while others suggest rather higher values. Such a lack of agreement raised a certain debate in the scientific community. In this paper, we aim to analyse the role of these properties on the behavior of asymmetric hyperonic matter. Using the formalism presented in Ref. (R.O. Gomes et al 2014}, which considers many-body forces contributions in the ...
Many-body central force potentials for tungsten
NASA Astrophysics Data System (ADS)
Bonny, G.; Terentyev, D.; Bakaev, A.; Grigorev, P.; Van Neck, D.
2014-07-01
Tungsten and tungsten-based alloys are the primary candidate materials for plasma facing components in fusion reactors. The exposure to high-energy radiation, however, severely degrades the performance and lifetime limits of the in-vessel components. In an effort to better understand the mechanisms driving the materials' degradation at the atomic level, large-scale atomistic simulations are performed to complement experimental investigations. At the core of such simulations lies the interatomic potential, on which all subsequent results hinge. In this work we review 19 central force many-body potentials and benchmark their performance against experiments and density functional theory (DFT) calculations. As basic features we consider the relative lattice stability, elastic constants and point-defect properties. In addition, we also investigate extended lattice defects, namely: free surfaces, symmetric tilt grain boundaries, the 1/2<1?1?1>{1?1?0} and 1/2<1?1?1> {1?1?2} stacking fault energy profiles and the 1/2<1?1?1> screw dislocation core. We also provide the Peierls stress for the 1/2<1?1?1> edge and screw dislocations as well as the glide path of the latter at zero Kelvin. The presented results serve as an initial guide and reference list for both the modelling of atomically-driven phenomena in bcc tungsten, and the further development of its potentials.
Another New Solvable Many-Body Model of Goldfish Type
NASA Astrophysics Data System (ADS)
Calogero, Francesco
2012-07-01
A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'') featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion of an arbitrary number N of unit-mass point-particles in a plane. The N (generally complex) values z_{n}( t) at time t of the N coordinates of these moving particles are given by the N eigenvalues of a time-dependent N× N matrix U( t) explicitly known in terms of the 2N initial data z_{n}( 0) and dot{z}_{n}(0) . This model comes in two different variants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''); for other special values of these parameters this property holds up to corrections vanishing exponentially as t? ? (''asymptotic isochrony''). Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.
Novel solvable extensions of the goldfish many-body model
NASA Astrophysics Data System (ADS)
Calogero, F.; Iona, S.
2005-10-01
A novel solvable extension of the goldfish N-body problem is presented. Its Newtonian equations of motion read ??n=2a?\\dot n?n+2?m =1,m?nN(?\\dot n-a?n2)(?\\dot m-a?m2)/(?n-?m), n =1,…,N, where a is an arbitrary (nonvanishing) constant and the rest of the notation is self-evident. The isochronous version of this model is characterized by the Newtonian equations of motion ??n-3i?\\zdot n-2?2zn=2a(\\zdot n-i?zn)zn+2?m =1,m?nN(\\zdot n-i?zn-azn2)(\\zdot m-i?zm-azm2)/(zn-zm), n =1,…,N, where ? is an arbitrary positive constant and the points zn(t) move now necessarily in the complex z-plane. The generic solution of this second model is completely periodic with a period Tk=kT which is an integer multiple k (not larger than N!, indeed generally much smaller) of the basic period T =2?/? and which is independent of the initial data (for sufficiently small, but otherwise arbitrary, changes of such data). These many-body models have an intriguing variety of equilibrium configurations (genuine: with no two particles sitting at the same place), but only for small values of N (N =2,3,4 for the first model, N =2,3,4,5 for the second). Other versions of these models are also discussed. The study of the behavior of the second, isochronous model around its equilibrium configurations yields some amusing diophantine results.
Many-body instabilities and mass generation in slow Dirac materials
NASA Astrophysics Data System (ADS)
Triola, Christopher; Zhu, Jian-Xin; Migliori, Albert; Balatsky, Alexander V.
2015-07-01
Some Kondo insulators are expected to possess topologically protected surface states with linear Dirac spectrum: the topological Kondo insulators. Because the bulk states of these systems typically have heavy effective electron masses, the surface states may exhibit extraordinarily small Fermi velocities that could force the effective fine structure constant of the surface states into the strong coupling regime. Using a tight-binding model, we study the many-body instabilities of these systems and identify regions of parameter space in which the system exhibits spin density wave and charge density wave order.
Chem. Rev. 1994, 94, 1975-1997 1975 Many-Body Effects in Intermolecular Forces
Elrod, Matthew J.
Chem. Rev. 1994, 94, 1975-1997 1975 Many-Body Effects in Intermolecular Forces Contents Matthew J, such that many relevant pair potential energy surfaces are now obtainable by inversion of experi- mental data to the actual many-body experimental result. Therefore, the study of many-body forces generally demands very
Symmetry-protected many-body Aharonov-Bohm effect
Santos, Luiz H.
It is known as a purely quantum effect that a magnetic flux affects the real physics of a particle, such as the energy spectrum, even if the flux does not interfere with the particle's path—the Aharonov-Bohm effect. Here ...
Tomsovic, Steve
as a sensitive measure capable of revealing phase space localization. Previously applied to chaotic quantum.e., disordered, interacting many-body, and/or simple chaotic systems. External param- eters. Molecular spectroscopy in external fields is an area of current interest and the response of a molecular
Quantum Simulation for Open-System Dynamics
NASA Astrophysics Data System (ADS)
Wang, Dong-Sheng; de Oliveira, Marcos Cesar; Berry, Dominic; Sanders, Barry
2013-03-01
Simulations are essential for predicting and explaining properties of physical and mathematical systems yet so far have been restricted to classical and closed quantum systems. Although forays have been made into open-system quantum simulation, the strict algorithmic aspect has not been explored yet is necessary to account fully for resource consumption to deliver bounded-error answers to computational questions. An open-system quantum simulator would encompass classical and closed-system simulation and also solve outstanding problems concerning, e.g. dynamical phase transitions in non-equilibrium systems, establishing long-range order via dissipation, verifying the simulatability of open-system dynamics on a quantum Turing machine. We construct an efficient autonomous algorithm for designing an efficient quantum circuit to simulate many-body open-system dynamics described by a local Hamiltonian plus decoherence due to separate baths for each particle. The execution time and number of gates for the quantum simulator both scale polynomially with the system size. Simulations are essential for predicting and explaining properties of physical and mathematical systems yet so far have been restricted to classical and closed quantum systems. Although forays have been made into open-system quantum simulation, the strict algorithmic aspect has not been explored yet is necessary to account fully for resource consumption to deliver bounded-error answers to computational questions. An open-system quantum simulator would encompass classical and closed-system simulation and also solve outstanding problems concerning, e.g. dynamical phase transitions in non-equilibrium systems, establishing long-range order via dissipation, verifying the simulatability of open-system dynamics on a quantum Turing machine. We construct an efficient autonomous algorithm for designing an efficient quantum circuit to simulate many-body open-system dynamics described by a local Hamiltonian plus decoherence due to separate baths for each particle. The execution time and number of gates for the quantum simulator both scale polynomially with the system size. DSW funded by USARO. MCO funded by AITF and Brazilian agencies CNPq and FAPESP through Instituto Nacional de Ciencia e Tecnologia-Informacao Quantica (INCT-IQ). DWB funded by ARC Future Fellowship (FT100100761). BCS funded by AITF, CIFAR, NSERC and USARO.
Observing the emergence of chaos in a many-particle quantum system
J. Tomkovi?; W. Muessel; H. Strobel; S. Löck; P. Schlagheck; R. Ketzmerick; M. K. Oberthaler
2015-09-06
Accessing the connection between classical chaos and quantum many-body systems has been a long-standing experimental challenge. Here, we investigate the onset of chaos in periodically driven two-component Bose-Einstein condensates, whose small quantum uncertainties allow for exploring the phase space with high resolution. By analyzing the uncertainties of time-evolved many-body states, we find signatures of elliptic and hyperbolic periodic orbits generated according to the Poincar\\'e-Birkhoff theorem, and the formation of a chaotic region at increasing driving strengths. The employed fluctuation analysis allows for probing the phase-space structure by use of only short-time quantum dynamics.
Relativistic many-body calculation of low-energy dielectronic resonances in Be-like carbon
NASA Astrophysics Data System (ADS)
Derevianko, A.; Dzuba, V. A.; Kozlov, M. G.
2010-08-01
We apply the relativistic configuration-interaction method coupled with the many-body perturbation theory (CI+MBPT) to describe low-energy dielectronic recombination. We combine the CI+MBPT approach with the complex rotation method (CRM) and compute the dielectronic recombination spectrum for Li-like carbon, which recombines into Be-like carbon. We demonstrate the utility and evaluate the accuracy of this newly developed CI+MBPT+CRM approach by comparing our results with the results of the previous high-precision study of the Ciii system [Mannervik , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.81.313 81, 313 (1998)].
Solvable Many-Body Models of Goldfish Type with One-, Two- and Three-Body Forces
NASA Astrophysics Data System (ADS)
Bihun, Oksana; Calogero, Francesco
2013-10-01
The class of solvable many-body problems ''of goldfish type'' is extended by including (the additional presence of) three-body forces. The solvable N-body problems thereby identified are characterized by Newtonian equations of motion featuring 19 arbitrary ''coupling constants''. Restrictions on these constants are identified which cause these systems - or appropriate variants of them - to be isochronous or asymptotically isochronous, i.e. all their solutions to be periodic with a fixed period (independent of the initial data) or to have this property up to contributions vanishing exponentially as t? ?.
TRIQS: A Toolbox for Research on Interacting Quantum Systems
Parcollet, Olivier; Ayral, Thomas; Hafermann, Hartmut; Krivenko, Igor; Messio, Laura; Seth, Priyanka
2015-01-01
We present the TRIQS library, a Toolbox for Research on Interacting Quantum Systems. It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way: e.g. Green's function containers, a generic Monte Carlo class, and simple interfaces to HDF5. TRIQS is a C++/Python library that can be used from either language. It is distributed under the GNU General Public License (GPLv3). State-of-the-art applications based on the library, such as modern quantum many-body solvers and interfaces between density-functional-theory codes and dynamical mean-field theory (DMFT) codes are distributed along with it.
Anomalous Diffusion and Griffiths Effects Near the Many-Body Localization Transition
NASA Astrophysics Data System (ADS)
Agarwal, Kartiek; Gopalakrishnan, Sarang; Knap, Michael; Müller, Markus; Demler, Eugene
2015-04-01
We explore the high-temperature dynamics of the disordered, one-dimensional X X Z model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.
The Hubbard Dimer: A density functional case study of a many-body problem
Carrascal, Diego; Smith, Justin C; Burke, Kieron
2015-01-01
This review explains the relationship between density functional theory and strongly correlated models using the simplest possible example, the two-site Hubbard model. The relationship to traditional quantum chemistry is included. Even in this elementary example, where the exact ground-state energy and site occupations can be found analytically, there is much to be explained in terms of the underlying logic and aims of Density Functional Theory. Although the usual solution is analytic, the density functional is given only implicitly. We overcome this difficulty using the Levy-Lieb construction to create a parametrization of the exact function with negligible errors. The symmetric case is most commonly studied, but we find a rich variation in behavior by including asymmetry, as strong correlation physics vies with charge-transfer effects. We explore the behavior of the gap and the many-body Green's function, demonstrating the `failure' of the Kohn-Sham method to reproduce the fundamental gap. We perform benchm...
Anomalous diffusion and griffiths effects near the many-body localization transition.
Agarwal, Kartiek; Gopalakrishnan, Sarang; Knap, Michael; Müller, Markus; Demler, Eugene
2015-04-24
We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features. PMID:25955037
Stochastic evaluation of second-order many-body perturbation energies.
Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So
2012-11-28
With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories. PMID:23205996
Many-body microhydrodynamics of colloidal particles with active boundary layers
Rajesh Singh; Somdeb Ghose; R. Adhikari
2015-07-13
Colloidal particles with active boundary layers - regions surrounding the particles where nonequilibrium processes produce large velocity gradients - are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between $N$ spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures.
Many-body Majorana operators and the equivalence of parity sectors
NASA Astrophysics Data System (ADS)
Kells, G.
2015-08-01
The one-dimensional p -wave topological superconductor model with open-boundary conditions is examined in its topological phase. Using the eigenbasis of the noninteracting system I show that, provided the interactions are local and do not result in a closing of the gap, then even and odd parity sectors are unitarily equivalent. Following on from this, it is possible to define two many-body operators that connect each state in one sector with a degenerate counterpart in the sector with opposite parity. This result applies to all states in the system and therefore establishes, for a long enough wire, that all even-odd eigenpairs remain essentially degenerate in the presence of local interactions. Building on this observation I then set out a full definition of the related many-body Majorana operators and point out that their structure cannot be fully revealed using cross-correlation data obtained from the ground-state manifold alone. Although all results are formulated in the context of the one-dimensional p -wave model, I argue why they should also apply to more realistic realizations (e.g., the multichannel p -wave wire and proximity coupled models) of topological superconductivity.
Non-perturbative approaches to problems in strongly-correlated many-body physics
NASA Astrophysics Data System (ADS)
Ma, Seungwook
The physics of strongly-correlated many-body systems pose formidable theoretical challenges. Methods based on perturbation theory break down due to the lack of a small parameter. This leads generically to the closure problem in a diagramatic expansion. In this thesis, we consider two such problems. The first involves the Mott insulator, a remarkable example of strong correlation effects among electrons leading to an insulating phase of what would otherwise be a metal. Of particular interest is the case when the ground state breaks neither the global rotational symmetry of the electronic spins nor the spatial symmetries of the lattice. Here the combination of strong coupling and quantum fluctuations leads to novel ground states with purely quantum mechanical origins. The second problem involves the statistics of dynamical systems. Although a set of nonlinear differential equations is deterministic and has a unique solution, it may be unstable to small triggering disturbances. Despite the unpredictability of individual trajectories, there may be reproducible and smoothly varying statistical properties. General methods to access directly statistical quantities are then necessary. In Part I of this thesis, we take the pragmatic view that the basic physics of spin liquids is contained in the one-band Hubbard model. For large on-site Coulomb repulsion, U ? infinity, we consider the Heisenberg limit at half-filling and include possible subleading exchange anisotropies of the Dzyaloshinskii-Moriya (DM) type. The work is motivated by two experimental realizations of layered spin-1/2 antiferromagnets. The first is Cs2CuCl4 where the spins reside on a spatially anisotropic triangular lattice. The second is ZnCu3(OH)6Cl2, called Herbertsmithite. Here, the spins reside on a spatially isotropic kagome lattice. Both are rare candidate materials in the search for spin liquid physics in two dimensions. To interpret experimentally measured quantities, we exactly diagonalize the Hamiltonian on small clusters. In addition, we utilize Gutzwiller-projected mean field theory to test whether various spin liquid states may be realized in nature. In Part II of this thesis, we apply the method of Hopf to low dimensional toy models of turbulence. A well-known example is the first-order system of three coupled nonlinear equations invented by Lorenz. The motivation was to find a simple model, amenable to fast numerical evaluation and capturing essential difficulties found in long-term weather prediction. In the hope of developing a statistical understanding of the Navier-Stokes equations, Hopf pioneered a functional integral method. The Hopf equations are in terms of a characteristic functional that determines the full time-independent problem and is equivalent to knowledge of the exact probability distribution. In our discussion, we focus on a simple chaotic dynamical system introduced by Orszag and McLaughlin and determine the exact Hopf characteristic functional.
Electro-optic and Many-body Effects on Optical Absorption of Twisted Bilayer Graphene
NASA Astrophysics Data System (ADS)
Lee, Kan-Heng; Huang, Lujie; Kim, Cheol-Joo; Park, Jiwoong
2015-03-01
In twisted bilayer graphene (tBLG), the interlayer rotation angle between the two graphene layers induces additional angle-dependent van Hove singularities (vHSs) in its band structure where the two Dirac cones from each layer intersect. These vHSs introduce extra angle-dependent absorption peaks in the optical absorption spectra of tBLG. Here, we experimentally investigate the effects of the overall doping and the interlayer potential on these interlayer absorption features at various angles. We independently tune the doping concentration of each layer with a newly-developed, optically transparent, dual-gate transistor geometry to perform simultaneous optical and electrical measurements. Our data show strong electro-optic phenomena in the optical absorption of tBLG: the peak energy and width of the interlayer resonance feature sensitively depends on the overall doping and interlayer potential. We explain our observation using a simple band picture as well as many-body effects. Our study provides a powerful experimental platform for studying more complicated structures such as rotated tri- and multi-layer graphene systems in the future. Moreover, the understanding of electro-optic and many-body effects in these materials opens up a way for novel electrochromic devices.
Many-body critical Casimir interactions in colloidal suspensions
Hobrecht, Hendrik
2015-01-01
We study the fluctuation-induced Casimir interactions in colloidal suspensions, especially between colloids immersed in a binary liquid close to its critical demixing point. To simulate these systems, we present a highly efficient cluster Monte Carlo algorithm based on geometric symmetries of the Hamiltonian. Utilizing the principle of universality, the medium is represented by an Ising system while the colloids are areas of spins with fixed orientation. Our results for the Casimir interaction potential between two particles at the critical point perfectly agree with the exact predictions. However, we find that in finite systems the behavior strongly depends on whether the medium order parameter is conserved and zero, or is allowed to fluctuate. Finally we present first results for the three-body Casimir interaction potential.