Many-particle Dynamics Research Articles

Stokesian dynamics with odd viscosity

Stokesian Dynamics is a well-established computational method for simulating dynamics of many particles suspended in a conventional passive fluid medium such as water. Active fluids composed of self-driving microscopic particles with broken time reversal symmetry permit the emergence of a so-called odd viscosity. In this work, we extended the conventional Stokesian Dynamics formalism to incorporate the additional hydrodynamic effects due to odd viscosity under a simplified quasi-two-dimensional case. This demonstrates that Stokesian Dynamics can be generalized to simulate collective behaviors of many particles suspended in an active fluid medium with both even and odd viscosity.

Exact solution of slow quench dynamics and nonadiabatic characterization of topological phases

Previous studies have shown that the bulk topology of single-particle systems can be captured by the band inversion surface or by the spin inversion surface emerging on the time-averaged spin polarization. Most of the studies, however, are based on the single-particle picture even though the systems are fermionic and multi-bands. Here, we study the slow quench dynamics of topological systems with all the valence bands fully occupied, and show that the concepts of band inversion surface and spin inversion surface are still valid. More importantly, the many-particle nonadiabatic quench dynamics is shown to be reduced to a new and nontrivial three-level Landau–Zener model. This nontrivial three-level Landau–Zener problem is then solved analytically by applying the integrability condition and symmetry considerations, and thus adds a new member to the few models that are exactly solvable. Based on the analytical results, the topological spin texture revealed by the time-averaged spin polarization can be applied to characterize the bulk topology and thus provides a direct comparison for future experiments.

New hyperbolic statistics for the equilibrium distribution function of interacting electrons

New statistics of a low-parameter distribution of the sech (ε, µ) type are presented, which reproduce the results of plasma simulation by the method of dynamics of many particles (DMP) with high accuracy. The distribution is based on a conceptual model of a two-component plasma — virtual quasiparticles of negative energy (exciton phase ε<0); the scattering region of positive energy (gas phase ε>0). Optimization and elementary estimates of the applicability of the sech (ε, µ) distribution statistics were made after the results of DMP experiments. The sech (ε,µ) distribution reduces the number of parameters of the three-piece DMP distribution from 4 energy diffusion coefficients (D1, D2, D3, D4) to two — the chemical potential µ and the asymmetry coefficient α. The functional relationship D1, D2, D3, D4 with the chemical potential of the system µ in the sech (ε, µ) distribution is introduced in a similar way to the Einstein relation between mobility and energy diffusion constants. The functional variety of the differential equation belongs to the family of elliptic functions. It is much wider than the hyperbolic solution given, which has significant physical application for complex values of the energy ε. The proposed simplified scheme grounded in the physical interpretation of negative energies can be written for the electrometric electrons of the atmosphere, which previously presented significant methodological difficulties. The chemical potentials of the fluid (metastable states) and gas phases are presented as functions of the plasma imperfection parameter. The problem is posed as an application to the problem of electrometric electrons in the atmosphere. The proposed distribution is not represented in mathematical statistics and statistical physics; it is new and extremely relevant.

Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy.

A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy. The method can also be applied to many-particle dynamics.

Toward a relativistic microscopic substantiation of thermodynamics: classical relativistic many-particle dynamics

An exact closed relativistic kinetic equation is derived for a system of identical classical particles interacting with each other through a scalar field. The law of variation of the energy of a system of particles in terms of the microscopic distribution function is obtained.

Apoptosis of moving nonorthogonal basis functions in many-particle quantum dynamics

Due to the exponential increase of the numerical effort with the number of degrees of freedom, moving basis functions have a long history in quantum dynamics. In addition, spawning of new basis functions is routinely applied. Here we advocate the opposite process: the programmed removal of motional freedom of selected basis functions. This is a necessity for converged numerical results with respect to the size of a non-orthogonal basis, because generically two or more states approach each other too closely early on, rendering unstable the matrix inversion, required to make the equations of motion explicit. Applications to the sub-Ohmic spin-boson model as well as to polaron dynamics in a Holstein molecular crystal model demonstrate the power of the proposed methodology.

Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales.

Despite considerable progress during the past decades in devising a semiclassical theory for classically chaotic quantum systems a quantitative semiclassical understanding of their dynamics at late times (beyond the so-called Heisenberg time T_{H}) is still missing. This challenge, corresponding to resolving spectral structures on energy scales below the mean level spacing, is intimately related to the quest for semiclassically restoring unitary quantum evolution. Guided through insights for quantum graphs we devise a periodic-orbit resummation procedure for spectra of quantum chaotic systems invoking periodic-orbit self-encounters as the structuring element of a hierarchical phase space dynamics. Quantum unitarity is reflected in real-valued spectral determinants with zeros giving discrete energy levels. We propose a way to purely semiclassically construct such real spectral determinants based on two major underlying mechanisms. (i) Complementary contributions to the spectral determinant from regrouped pseudo-orbits of duration T<T_{H} and T_{H}-T are complex conjugate to each other. (ii) Contributions from long periodic orbits involving multiple traversals along shorter orbits cancel out. We furthermore discuss implications for interacting N-particle quantum systems with a chaotic classical large-N limit that have recently attracted particular interest in the context of many-body quantum chaos.

Rheology of symmetric diblock copolymers

Using large-scale simulations with the graphics processing unit (GPU) accelerated Highly Optimized Object-oriented Many-particle Dynamics (HOOMD)-blue software we investigate the anisotropic, dynamic-mechanical properties of lamellae-forming diblock copolymer melts. Both, the shear-stress autocorrelation function in equilibrium as well as stress-controlled simulations of shear flow are considered. The latter are implemented in (HOOMD)-blue via reverse nonequilibrium molecular dynamics simulation (RNEMDS).We find that copolymer lamellae that are perpendicularly oriented to the shear flow have similar rheological properties than unstructured homopolymer melts. Copolymer lamellae with the metastable parallel and the unstable transverse orientation exhibit similar dynamic-mechanical behavior in the linear regime. Most notably, they are characterized by a high dissipation.(RNEMDS) enables the study of oscillatory shear flow as well as the investigation of nonlinear rheology. Our simulation results for a soft, coarse-grained model at very high frequencies indicate that the finite speed of stress propagation has to be accounted for in the quantitative analysis, and we devise an analytic prediction for the nonlinear velocity and spatially varying stress profiles as a function of the loss and storage moduli.

Full-Counting Many-Particle Dynamics: Nonlocal and Chiral Propagation of Correlations.

The ability to measure single quanta allows the complete characterization of small quantum systems known as full-counting statistics. Quantum gas microscopy enables one to observe many-body systems at the single-atom precision. We extend the idea of full-counting statistics to nonequilibrium open many-particle dynamics and apply it to discuss the quench dynamics. By way of illustration, we consider an exactly solvable model to demonstrate the emergence of unique phenomena such as nonlocal and chiral propagation of correlations, leading to a concomitant oscillatory entanglement growth. We find that correlations can propagate beyond the conventional maximal speed, known as the Lieb-Robinson bound, at the cost of probabilistic nature of quantum measurement. These features become most prominent at the real-to-complex spectrum transition point of an underlying parity-time-symmetric effective non-Hermitian Hamiltonian. A possible experimental situation with quantum gas microscopy is discussed.

Colloidal particle electrorotation in a nonuniform electric field.

A model to study the dynamics of colloidal particles in nonuniform electric fields is proposed. For an isolated sphere, the conditions and threshold for sustained (Quincke) rotation in a linear direct current (dc) field are determined. Particle dynamics becomes more complex with increasing electric field strength, changing from steady spinning around the particle center to time-dependent orbiting motion around the minimum field location. Pairs of particles exhibit intricate trajectories, which are a combination of translation, due to dielectrophoresis, and rotation, due to the Quincke effect. Our model provides a basis to study the collective dynamics of many particles in a general electric field.

Many-particle interference in a two-component bosonic Josephson junction: an all-optical simulation

We conceive an all-optical representation of the dynamics of two distinct types of interacting bosons in a double well by an array of evanescently coupled photonic waveguides. Many-particle interference effects are probed for various interaction strengths by changing the relative abundance of the particle species and can be readily identified by monitoring the propagation of the light intensity across the waveguide array. In particular, we show that finite inter-particle interaction strengths reduce the many-particle interference contrast by dephasing. A general description of the many-particle dynamics for arbitrary initial states is given in terms of two coupled spins by generalising the Schwinger representation to two particle species.

A perspective on quantum integrability in many-body-localized and Yang-Baxter systems.

Two of the most active areas in quantum many-particle dynamics involve systems with an unusually large number of conservation laws. Many-body-localized systems generalize ideas of Anderson localization by disorder to interacting systems. While localization still exists with interactions and inhibits thermalization, the interactions between conserved quantities lead to some dramatic differences from the Anderson case. Quantum integrable models such as the XXZ spin chain or Bose gas with delta-function interactions also have infinite sets of conservation laws, again leading to modifications of conventional thermalization. A practical way to treat the hydrodynamic evolution from local equilibrium to global equilibrium in such models is discussed. This paper expands upon a presentation at a discussion meeting of the Royal Society on 7 February 2017. The work described was carried out with a number of collaborators, including Jens Bardarson, Vir Bulchandani, Roni Ilan, Christoph Karrasch, Siddharth Parameswaran, Frank Pollmann and Romain Vasseur.This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.

Simulations of Model Microswimmers with Fully Resolved Hydrodynamics

Swimming microorganisms, which include bacteria, algae, and spermatozoa, play a fundamental role in most biological processes. These swimmers are a special type of active particle, that continuously convert local energy into propulsive forces, thereby allowing them to move through their surrounding fluid medium. While the size, shape, and propulsion mechanism vary from one organism to the next, they share certain general characteristics: they exhibit force-free motion and they swim at a small Reynolds number. To study the dynamics of such systems, we use the squirmer model, which provides an ideal representation of swimmers as spheroidal particles that propel owing to a modified boundary condition at their surface. We have considered the single-particle and many-particle dynamics of swimmers in bulk and confined systems using the smoothed profile method, which allows us to efficiently solve the coupled particle-fluid problem. For the single-particle dynamics, we studied the diffusive behavior caused by th...

On optimal currents of indistinguishable particles

We establish a mathematically rigorous, general and quantitative framework to describe currents of non- (or weakly) interacting, indistinguishable particles driven far from equilibrium. We derive tight upper and lower bounds for the achievable fermionic and bosonic steady state current, respectively, which can serve as benchmarks for special cases of interacting many-particle dynamics. For fermionic currents, we identify a symmetry-induced enhancement mechanism in parameter regimes where the coupling between system and reservoirs is weak. This mechanism is broadly applicable provided the inter-particle interaction strength is small as compared to typical exchange interactions.

Charging of a rodlike grain in plasma flow

In present work on the basis of numerical modeling by the dynamics of many particles, a self-consistentproblem of the formation of a charge accumulated by a dusty particle of a rodlike shape in a twotemperatureplasma flow is considered. An analytical model useful for understanding the phenomenon ofion focusing and its effect on the formation of the surface charge of a needle was considered. Pairwise radialcorrelation functions evaluated in the approximation of binary interaction for moving particles with astationary Coulomb center. Using conservation law for the momentum ion velocity component has beendetermined. It was noticed that electron shielding does not influence on the ion focusing density peak value.In that reason ion focusing parameters in the concrete doesn’t depend on the electron screening Debyeradius. A system with Coulomb particles containing moving point particles, ions and electrons, and fixedspheres have been chosen. The cases of dielectric and metallic dust grains having different orientationswith respect to the flow direction are considered.

Progress towards quantum-enhanced interferometry with harmonically trapped quantum matter-wave bright solitons

We model the dynamics of attractively interacting ultracold bosonic atoms in a quasi-one-dimensional wave-guide with additional harmonic trapping. Initially, we prepare the system in its ground state and then shift the zero of the harmonic trap and switch on an additional narrow scattering potential near the center of the trap. After colliding with the barrier twice, we propose to measure the number of atoms opposite to the initial condition. Quantum-enhanced interferometry with quantum bright solitons allows us to predict detection of an offset of the scattering potential with considerably increased precision as compared to single-particle experiments. In a future experimental realization this might lead to measurement of weak forces caused, for example, by small horizontal gradients in the gravitational potential - with a resolution of several micrometers given essentially by the size of the solitons. Our numerical simulations are based on the rigorously proved effective potential approach developed in [Phys. Rev. Lett. 102, 010403 (2009) and Phys. Rev. Lett. 103, 210402 (2009)]. We choose our parameters such that the prerequisite of the proof (that the solitons cannot break apart, for energetic reasons) is always fulfilled, thus exploring a parameter regime inaccessible to the mean-field description via the Gross-Pitaevskii equation due to Schrodinger-cat states occurring in the many-particle quantum dynamics.

Bose-Einstein condensates with balanced gain and loss beyond mean-field theory

Most of the work done in the field of Bose-Einstein condensates with balanced gain and loss has been performed in the mean-field approximation using the PT-symmetric Gross-Pitaevskii equation. In this work we study the many-particle dynamics of a two-mode condensate with balanced gain and loss described by a master equation in Lindblad form whose purity periodically drops to small values but then is nearly completely restored. This effect cannot be covered by the mean-field approximation, in which a completely pure condensate is assumed. We present analytic solutions for the dynamics in the non-interacting limit and use the Bogoliubov backreaction method to discuss the influence of the on-site interaction. Our main result is that the strength of the purity revivals is almost exclusively determined by the strength of the gain and loss and is independent of the amount of particles in the system and the interaction strength. For larger particle numbers, however, strong revivals are shifted towards longer times, but by increasing the interaction strength these strong revivals again occur earlier.

Statistical benchmark for BosonSampling

Boson samplers—set-ups that generate complex many-particle output states through the transmission of elementary many-particle input states across a multitude of mutually coupled modes—promise the efficient quantum simulation of a classically intractable computational task, and challenge the extended Church–Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, one crucial problem remains: how to certify that a given experimental measurement record unambiguously results from enforcing the claimed dynamics, on bosons, fermions or distinguishable particles? Here we offer a statistical solution to the certification problem, identifying an unambiguous statistical signature of many-body quantum interference upon transmission across a multimode, random scattering device. We show that statistical analysis of only partial information on the output state allows to characterise the imparted dynamics through particle type-specific features of the emerging interference patterns. The relevant statistical quantifiers are classically computable, define a falsifiable benchmark for BosonSampling, and reveal distinctive features of many-particle quantum dynamics, which go much beyond mere bunching or anti-bunching effects.

Out-of-equilibrium fluctuations in stochastic long-range interacting systems

For a many-particle system with long-range interactions and evolving under stochastic dynamics, we study for the first time the out-of-equilibrium fluctuations of the work done on the system by a time-dependent external force. For equilibrium initial conditions, the work distributions for a given protocol of variation of the force in time and the corresponding time-reversed protocol exhibit a remarkable scaling and a symmetry when expressed in terms of the average and the standard deviation of the work. The distributions of the work per particle predict, by virtue of the Crooks fluctuation theorem, the equilibrium free-energy density of the system. For a large number N of particles, the latter is in excellent agreement with the value computed by considering the Langevin dynamics of a single particle in a self-consistent mean field generated by its interaction with other particles. The agreement highlights the effective mean-field nature of the original many-particle dynamics for large N. For initial conditions in non-equilibrium stationary states (NESSs), we study the distribution of a quantity similar to dissipated work that satisfies the non-equilibrium generalization of the Clausius inequality, namely, the Hatano-Sasa equality, for transitions between NESSs. Besides illustrating the validity of the equality, we show that the distribution has exponential tails that decay differently on the left and on the right.

Hydrodynamic coupling of particle inclusions embedded in curved lipid bilayer membranes.

We develop theory and computational methods to investigate particle inclusions embedded within curved lipid bilayer membranes. We consider the case of spherical lipid vesicles where inclusion particles are coupled through (i) intramembrane hydrodynamics, (ii) traction stresses with the external and trapped solvent fluid, and (iii) intermonolayer slip between the two leaflets of the bilayer. We investigate relative to flat membranes how the membrane curvature and topology augment hydrodynamic responses. We show how both the translational and rotational mobility of protein inclusions are effected by the membrane curvature, ratio of intramembrane viscosity to solvent viscosity, and intermonolayer slip. For general investigations of many-particle dynamics, we also discuss how our approaches can be used to treat the collective diffusion and hydrodynamic coupling within spherical bilayers.