Dynamics Of Many-body Systems Research Articles

Information scrambling dynamics in a fully controllable quantum simulator

Quantum information scrambling has received tremendous attention owing to its key concept in the fields of quantum chaos and quantum gravity. Here, with exploiting a fully controllable superconducting quantum processor, we study the verified scrambling in a 1D spin chain by an analog superconducting quantum simulator with the signs and values of individual driving and coupling terms fully controllable. By engineering opposite Hamiltonians on two subsystems, we measure the temporal and spatial patterns of out-of-time ordered correlators (OTOC), with the Hamiltonian mismatch and the decoherence extracted quantitatively from the scrambling dynamics, providing a benchmarking tool for probing not only the spatial but the temporal patterns of scrambling dynamics in many-body systems. Our work demonstrates the superconducting system with strong controllability as a powerful quantum simulator.

Coherent structure formation via spatial phase coupling in two-dimensional (potential) vorticity-conserved systems

We employ the phase synchronization concept, which is universally adopted to study collective dynamics in many-body systems, to investigate the formation mechanism of coherent structure in a two-dimensional (potential) vorticity conserved system. It is shown that the gradient of mean (potential) vorticity can mediate ``attractive'' coupling among local vortex excitations, so that the vortices get synchronized and a large coherent structure then forms. The phase synchronization concept develops a method for studying self-organization processes in fluid turbulence.

Tails of Instability and Decay: a Hydrodynamic Perspective

In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and life-time of the particle, observed in scattering events. In this paper, we uncover new, dynamical signatures of unstable excitations and show that they have a strong effect on the non-equilibrium properties of QFT. Focusing on a 1+1D integrable model, and using the theory of Generalized Hydrodynamics, we study the formation and decay of unstable particles by analysing the release of hot matter into a low-temperature environment. We observe the formation of tails and the decay of the emitted nonlinear waves, in sharp contrast to the situation without unstable excitations. We also uncover a new phenomenon by which a wave of a stable population of unstable particles may persist without decay for long times. We expect these signatures of the presence of unstable particles to have a large degree of universality. Our study shows that the out-of-equilibrium dynamics of many-body systems can be strongly affected not only by the spectrum, but also by excitations with finite life-times.

Linear and nonlinear response for radiative heat transfer in many-body systems

A theory of temperature dynamics in many-body systems driven by time-dependent external sources is introduced. The formalism based on the combination of the perturbation theory and the fluctuational-electrodynamics approach in many-body systems. By using response theory, explicit formula for the temperature and phase shifts is derived and expressed in terms of the amplitude and phase of external power sources. Although the proposed method is highly efficient because it can skip the transient response, it is valid when external powers are weak. As an illustration of this theoretical framework, we have shown the dynamics of temperatures in one, two, and three degree of freedom systems driven by sine wave input powers. Finally, we highlighted some emergent phenomena arising from purely dynamical many-body effects, including amplification, attenuation, delaying or accelerating temperature responses. This work could find important applications in the domain of dynamical thermal management at the nanoscale.

Electromagnetically induced transparency of interacting Rydberg atoms with two-body dephasing.

We study electromagnetically induced transparency in a three-level ladder type configuration in ultracold atomic gases, where the upper level is an electronically highly excited Rydberg state. An effective distance dependent two-body dephasing can be induced in a regime where dipole-dipoles interaction couple nearly degenerate Rydberg pair states. We show that strong two-body dephasing can enhance the excitation blockade of neighboring Rydberg atoms. Due to the dissipative blockade, transmission of the probe light is reduced drastically by the two-body dephasing in the transparent window. The reduction of transmission is accompanied by a strong photon-photon anti-bunching. Around the Autler-Townes doublets, the photon bunching is amplified by the two-body dephasing, while transmission is largely unaffected. Besides relevant to the ongoing Rydberg atom studies, our study moreover provides a setting to explore and understand two-body dephasing dynamics in many-body systems.

Molecular Docking of a Bio Material [1-{[(Z)-Cyclopentylidene] Amino}-3-Phenylthiourea] by First Principles Study

Molecular Docking and complete quantum chemical studies of 1-{[(Z)-Cyclopentylidene] amino}-3-phenylthiourea have been done by using DFT/ B3LYP method and 6-311 G (d, p) as the basis set. We have compared optimized geometry of title molecule with experimental data. A detailed interpretation of the vibrational assignments of title molecule is reported. Molecular Electrostatic Potential (MESP) generated by a chemical species is widely used as a tool for exploring its properties and locating potential sites for interaction with other moieties. Nonlinear optics (NLO) is the branch of optics that describes the behavior of materials in nonlinear media. In quantum chemistry, a natural bond orbital or NBO is a calculated bonding orbital with maximum electron density. Time-dependent density functional theory (TDDFT) is a quantum mechanical theory used in physics and chemistry to investigate the properties and dynamics of many-body systems in the presence of time-dependent potentials, such as electric or magnetic fields.The electronic properties of title molecule are discussed with help of molecular FHOMO, FLUMO composition, band gap, and MESP plots. The NLO, NBO, UV spectra of title molecule also calculated with same level of theory. Some biological parameter Log P and Log S are also calculated which suggests that the title molecule have good ability to deliver drugs in various diseases.

Competing coherent and dissipative dynamics close to quantum criticality

We investigate the competition of coherent and dissipative dynamics in many-body systems at continuous quantum transitions. We consider dissipative mechanisms that can be effectively described by Lindblad equations for the density matrix of the system. The interplay between the critical coherent dynamics and dissipation is addressed within a dynamic finite-size scaling framework, which allows us to identify the regime where they develop a nontrivial competition. We analyze protocols that start from critical many-body ground states and put forward general dynamic scaling behaviors involving the Hamiltonian parameters and the coupling associated with the dissipation. This scaling scenario is supported by a numerical study of the dynamic behavior of a one-dimensional lattice fermion gas undergoing a quantum Ising transition in the presence of dissipative mechanisms such as local pumping, decaying, and dephasing.

A Universal Operator Growth Hypothesis

We present a hypothesis for the universal properties of operators evolving under Hamiltonian dynamics in many-body systems. The hypothesis states that successive Lanczos coefficients in the continued fraction expansion of the Green's functions grow linearly with rate $\alpha$ in generic systems, with an extra logarithmic correction in 1d. The rate $\alpha$ --- an experimental observable --- governs the exponential growth of operator complexity in a sense we make precise. This exponential growth even prevails beyond semiclassical or large-$N$ limits. Moreover, $\alpha$ upper bounds a large class of operator complexity measures, including the out-of-time-order correlator. As a result, we obtain a sharp bound on Lyapunov exponents $\lambda_L \leq 2 \alpha$, which complements and improves the known universal low-temperature bound $\lambda_L \leq 2 \pi T$. We illustrate our results in paradigmatic examples such as non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models. Finally we use the hypothesis in conjunction with the recursion method to develop a technique for computing diffusion constants.

Dynamical BCS Theory of a Two-Dimensional Attractive Fermi Gas: Effective Interactions from Quantum Monte Carlo Calculations

The primary work presented in this paper focuses on the calculation of density-density dynamical correlations in an attractive two dimensional Fermi gas in several physically interesting regimes, including the strongly correlated BEC-BCS crossover regime. We use state-of-the-art dynamical BCS theory and we address the possibility to renormalize the interaction strength, using unbiased Quantum Monte Carlo results as an asset to validate the predictions. We propose that a suitable interplay between dynamical BCS theory, which is computationally very cheap and yields results directly in real time domain, and Quantum Monte Carlo methods, which are exact but way more demanding and limited to imaginary time domain, can be a very promising idea to study dynamics in many body systems. We illustrate the idea and provide quantitative results for a few values of the interaction strength in the cold gas.

Multipartite entanglement dynamics in a regular-to-ergodic transition: Quantum Fisher information approach

The characterization of entanglement is a central problem for the study of quantum many-body dynamics. Here, we propose the quantum Fisher information as a useful tool for the study of multipartite-entanglement dynamics in many-body systems. We illustrate this by considering the regular-to-ergodic transition in the Dicke model---a fully-connected spin model showing quantum thermalization above a critical interaction strength. We show that the QFI has a rich dynamical behavior which drastically changes across the transition. In particular, the asymptotic value of the QFI, as well as its characteristic timescales, witness the transition both through their dependence on the interaction strength and through the scaling with the system size. Since the QFI also sets the ultimate bound for the precision of parameter estimation, it provides a metrological perspective on the characterization of entanglement dynamics in many-body systems. Here we show that quantum ergodic dynamics allows for a much faster production of metrologically useful states.

Quench dynamics of a dissipative Rydberg gas in the classical and quantum regimes

Understanding the non-equilibrium behavior of quantum systems is a major goal of contemporary physics. Much research is currently focused on the dynamics of many-body systems in low-dimensional lattices following a quench, i.e., a sudden change of parameters. Already such a simple setting poses substantial theoretical challenges for the investigation of the real-time post-quench quantum dynamics. In classical many-body systems the Kolmogorov-Mehl-Johnson-Avrami model describes the phase transformation kinetics of a system that is quenched across a first order phase transition. Here we show that a similar approach can be applied for shedding light on the quench dynamics of an interacting gas of Rydberg atoms, which has become an important experimental platform for the investigation of quantum non-equilibrium effects. We are able to gain an analytic understanding of the time-evolution following a sudden quench from an initial state devoid of Rydberg atoms and identify strikingly different behaviors of the excitation growth in the classical and quantum regimes. Our approach allows us to describe quenches near a non-equilibrium phase transition and provides an approximate analytic solution deep in the quantum domain.

Nonlinear entangled quantum dynamics in many-body systems with strong electron correlation

A quantum impurity system out of equilibrium comprises two metallic reservoirs with different chemical potentials and one mediating spin impurity between them. We study the highly nonlinear tunneling conductance of this system, and clarify that three coherent peaks, one zero-bias peak and two side peaks, naturally appear in the tunneling conductance. We use the Liouvillian approach, in which a complete set of basis operators is available, and construct a Liouville matrix to obtain Green’s function at the mediating site. We show that the two coherent side peaks are the outcome of steady-state nonequilibrium combined with strong electron correlation at the mediating site. Tunneling in the quantum impurity system out of equilibrium is performed by an entangled state which is a linear combination of two Kondo singlets formed by the spin at the mediating site and the coherent spins in each reservoir. The fluctuation by incoherent spins is also included. The spectral weights and positions of the three coherent peaks are analytically discussed via atomic limit analysis. Our theoretical results well fit experimental data obtained for quantum point contacts with symmetric and asymmetric Kondo couplings.

Entanglement dynamics in quantum many-body systems

The dynamics of entanglement has recently been realized as a useful probe in studying ergodicity and its breakdown in quantum many-body systems. In this paper, we study theoretically the growth of entanglement in quantum many-body systems and propose a method to measure it experimentally. We show that entanglement growth is related to the spreading of local operators in real space. We present a simple toy model for ergodic systems in which linear spreading of operators results in a universal, linear in time growth of entanglement for initial product states, in contrast with 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 several copies of the original system, in which connections are controlled by a quantum switch (two-level system). By measuring only the switch's dynamics, the growth of the R\'enyi entropies can be extracted. Our work provides a way of understanding entanglement dynamics in many-body systems, and to directly measure its growth in time via a single local measurement.

Short Range Correlations: The Important Role of Few-Body Dynamics in Many-Body Systems

For many-body systems with short range interaction a series of relations were derived connecting many properties of the system to the dynamics of a closely packed few-body subsystems. Some of these relations were experimentally verified in ultra cold atomic gases. Here we shall review the implications of these developments on our understanding of nuclear one and two-body momentum distributions, and on the electron scattering Coulomb sum rule.

Double-slit interference with charged particles: density matrices and decoherence from time-dependent quantum Monte Carlo

In this paper we apply the time-dependent quantum Monte Carlo (TDQMC) method to explore a modified single- and double-slit diffraction of matter waves. By using a simplified model of two electrons prepared in the ground state of an atom (molecule) and then suddenly released we are able to calculate the diffraction patterns in one spatial dimension in close correspondence with the numerically exact results. Through the Coulomb repulsion the one electron serves as an environment for the other, thus introducing decoherence in the quantum state which is easily quantified. It is demonstrated that the set of single particle wave functions yield by TDQMC can be used to directly construct a density matrix for that particle without tracing out the other constituents from the density matrix of the whole system. In this way it is possible to build explicitly time-dependent density matrices for different components of a complex quantum system straight within the TDQMC algorithm which may widen our understanding of quantum dynamics in many-body systems.

Entanglement dynamics of many-body systems: Analytical results

We consider a many-body system consisting of a harmonic oscillator linearly coupled to $N$ others and solve the corresponding dynamical problem analytically. Initially, the main oscillator is prepared in a superposition of two coherent states and the $N$ others in the ground states. We divide this system in arbitrary three partitions and the entanglement dynamics between any of these partitions is quantified. We show that the residual entanglement of the tripartite system is always present. Besides, the concurrence of any two partitions depends on the overlap between the two coherent states forming the initial superposition of the main oscillator and the distribution of excitations in the partitions. Finally, we obtain a hierarchy of entanglement between the central oscillator and partitions formed by the other oscillators. For long times the excitations of the main oscillator are completely transferred to the $N$ others and these are found entangled.

Kinetic phase transition with global coupling in the resonantly driven atomic trap

We present an experimental observation and comprehensive theory that address the effect of interaction on the phase transition in a many-body system, which is far from equilibrium and does not have detailed balance. In the resonantly driven cold atomic trap, we observe kinetic phase transition (KPT) that is manifested by substantial enhancement of fluctuations, similar to the first-order phase transition in thermal equilibrium. Moreover, we can control the attractive interaction between atoms trapped in the coexisting states by adjusting the total number of atoms, which induces shift of the phase boundaries of KPT. The demonstrated effect is the many-body analogue of KPT that was previously predicted and observed in a single-driven oscillator. Our work provides a unique model platform for quantitative study of nonequilibrium nonlinear dynamics in many-body systems.

Scaling of quantum Zeno dynamics in many-body systems

We study the quantum Zeno effect (QZE) in a many-body system, namely the Lipkin–Meshkov–Glick model, coupled to a central qubit. Our result shows that in order to observe QZE in the symmetry-broken phase of the model, the frequency of the projective measurement should be of comparable order to that of the system sizes. However, in the polarized phase of the model, the QZE can be easily observed by frequent measurements.

Simulation of environmental effects on coherent quantum dynamics in many-body systems.

In this paper we describe an application of the trajectory-based semiclassical Liouville method for modeling coherent molecular dynamics on multiple electronic surfaces to the treatment of the evolution and decay of quantum electronic coherence in many-body systems. We consider a model representing the coherent evolution of quantum wave packets on two excited electronic surfaces of a diatomic molecule in the gas phase and in rare gas solvent environments, ranging from small clusters to a cryogenic solid. For the gas phase system, the semiclassical trajectory method is shown to reproduce the evolution of the electronic-nuclear coherence nearly quantitatively. The dynamics of decoherence are then investigated for the solvated systems using the semiclassical approach. It is found that, although solvation in general leads to more rapid and extensive loss of quantum coherence, the details of the coupled system-bath dynamics are important, and in some cases the environment can preserve or even enhance quantum coherence beyond that seen in the isolated system.

Theoretical and computational models of biological ion channels

The goal of this review is to establish a broad and rigorous theoretical framework to describe ion permeation through biological channels. This framework is developed in the context of atomic models on the basis of the statistical mechanical projection-operator formalism of Mori and Zwanzig. The review is divided into two main parts. The first part introduces the fundamental concepts needed to construct a hierarchy of dynamical models at different level of approximation. In particular, the potential of mean force (PMF) as a configuration-dependent free energy is introduced, and its significance concerning equilibrium and non-equilibrium phenomena is discussed. In addition, fundamental aspects of membrane electrostatics, with a particular emphasis on the influence of the transmembrane potential, as well as important computational techniques for extracting essential information from all-atom molecular dynamics (MD) simulations are described and discussed. The first part of the review provides a theoretical formalism to 'translate' the information from the atomic structure into the familiar language of phenomenological models of ion permeation. The second part is aimed at reviewing and contrasting results obtained in recent computational studies of three very different channels: the gramicidin A (gA) channel, which is a narrow one-ion pore (at moderate concentration), the KcsA channel from Streptomyces lividans, which is a narrow multi-ion pore, and the outer membrane matrix porin F (OmpF) from Escherichia coli, which is a trimer of three beta-barrel subunits each forming wide aqueous multi-ion pores. Comparison with experiments demonstrates that current computational models are approaching semi-quantitative accuracy and are able to provide significant insight into the microscopic mechanisms of ion conduction and selectivity. We conclude that all-atom MD with explicit water molecules can represent important structural features of complex biological channels accurately, including such features as the location of ion-binding sites along the permeation pathway. We finally discuss the broader issue of the validity of ion permeation models and an outlook to the future.