Transport Properties and Control in Low-Dimensional Quantum Many-Body Systems (abstract)

2009 ◽  
Author(s):  
Lea F. Santos ◽  
Beverly Karplus Hartline ◽  
Renee K. Horton ◽  
Catherine M. Kaicher
Keyword(s):  
Transport Properties ◽  
Many Body ◽  
Many Body Systems ◽  
Low Dimensional ◽  
And Control

scholarly journals Applications of fidelity measures to complex quantum systems

2016 ◽  
Vol 374 (2069) ◽  
pp. 20150153 ◽  
Author(s):  
Sandro Wimberger
Keyword(s):  
Cold Atoms ◽  
Dimensional System ◽  
Many Body ◽  
Practical Applications ◽  
Dynamical Regimes ◽  
Many Body Systems ◽  
Fidelity Measures ◽  
The Stability ◽  
Low Dimensional ◽  
Quantum Motion

We revisit fidelity as a measure for the stability and the complexity of the quantum motion of single-and many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular–chaotic phase space.

scholarly journals Machine learning active-nematic hydrodynamics

2021 ◽  
Vol 118 (10) ◽  
pp. e2016708118
Author(s):  
Jonathan Colen ◽  
Ming Han ◽  
Rui Zhang ◽  
Steven A. Redford ◽  
Linnea M. Lemma ◽  
...  
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Initial Conditions ◽  
Molecular Motor ◽  
Machine Learning Algorithms ◽  
Many Body ◽  
Hydrodynamic Parameters ◽  
Many Body Systems ◽  
And Control ◽  
Macroscopic Parameters

Hydrodynamic theories effectively describe many-body systems out of equilibrium in terms of a few macroscopic parameters. However, such parameters are difficult to determine from microscopic information. Seldom is this challenge more apparent than in active matter, where the hydrodynamic parameters are in fact fields that encode the distribution of energy-injecting microscopic components. Here, we use active nematics to demonstrate that neural networks can map out the spatiotemporal variation of multiple hydrodynamic parameters and forecast the chaotic dynamics of these systems. We analyze biofilament/molecular-motor experiments with microtubule/kinesin and actin/myosin complexes as computer vision problems. Our algorithms can determine how activity and elastic moduli change as a function of space and time, as well as adenosine triphosphate (ATP) or motor concentration. The only input needed is the orientation of the biofilaments and not the coupled velocity field which is harder to access in experiments. We can also forecast the evolution of these chaotic many-body systems solely from image sequences of their past using a combination of autoencoders and recurrent neural networks with residual architecture. In realistic experimental setups for which the initial conditions are not perfectly known, our physics-inspired machine-learning algorithms can surpass deterministic simulations. Our study paves the way for artificial-intelligence characterization and control of coupled chaotic fields in diverse physical and biological systems, even in the absence of knowledge of the underlying dynamics.

Oxides: An answer to the qubit problem?

2019 ◽  
Vol 33 (14) ◽  
pp. 1930003
Author(s):  
Amit Dey ◽  
Sudhakar Yarlagadda
Keyword(s):  
Electronic Devices ◽  
Small Scale ◽  
Double Quantum ◽  
Phonon Coupling ◽  
Many Body ◽  
Double Quantum Dots ◽  
Electron Phonon Coupling ◽  
Low Dimensional ◽  
And Control ◽  
Many Body Interactions

Low-dimensional complex oxides offer new opportunities for small-scale electronic devices where diverse spin, charge and orbital correlations can be suitably adapted by manipulating many-body interactions, geometries, disorder, fields, strain, etc. Therefore, oxides may be viewed as one of the promising candidates for replacing semiconductors in future devices. Maintaining coherence and control in a qubit is an important necessity for quantum computation. In this review, we discuss an example of oxide devices: decoherence-free oxide-based qubits. We present recent progress in demonstrating that long coherence times can be achieved at easily accessible temperatures in charge qubits of oxide double quantum dots. For treating strong coupling to the environment, we describe a nonperturbative approach that is useful for oxides. We illustrate ways to enhance the coherence times: increasing the electron–phonon coupling, detuning the dots to a fraction of the optical phonon energy, decreasing the temperature or reducing the adiabaticity.

New Frontiers in Controlling the Motion of Matter with Light: From Single Atoms to Neurons

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4100-4100
Author(s):  
Mark G. Raizen
Keyword(s):  
Quantum Dynamics ◽  
Atomic Level ◽  
Many Body ◽  
Future Directions ◽  
The Past ◽  
Dynamics And Control ◽  
Weak Light ◽  
Many Body Systems ◽  
Neuron Growth ◽  
And Control

In this talk I will discuss recent experiments in my group on the interactions and control of matter with light. At the atomic level we have been studying the interface between quantum mechanics and nonlinear dynamics. I will describe some recent experiments on atomic motion in "optical billiards", a new system that we developed, and indicate some future directions for quantum dynamics and control in many-body systems. In the past year we have also extended our work to the realm of biophysics in collaboration with the group of Josef Kas. We have shown experimentally that we can use weak light forces to precisely guide the direction of neuron growth, which opens many exciting directions for the future.

scholarly journals Gaussian Information Bottleneck and the Non-Perturbative Renormalization Group

2021 ◽  
Author(s):  
Adam Gordon Kline ◽  
Stephanie Palmer
Keyword(s):  
Renormalization Group ◽  
Large Scale ◽  
Dimensional Structure ◽  
Many Body ◽  
Closed Form Solutions ◽  
Information Bottleneck ◽  
Perturbative Renormalization ◽  
Optimal Encoding ◽  
Many Body Systems ◽  
Low Dimensional

Abstract The renormalization group (RG) is a class of theoretical techniques used to explain the collective physics of interacting, many-body systems. It has been suggested that the RG formalism may be useful in finding and interpreting emergent low-dimensional structure in complex systems outside of the traditional physics context, such as in biology or computer science. In such contexts, one common dimensionality-reduction framework already in use is information bottleneck (IB), in which the goal is to compress an ``input'' signal X while maximizing its mutual information with some stochastic ``relevance'' variable Y. IB has been applied in the vertebrate and invertebrate processing systems to characterize optimal encoding of the future motion of the external world. Other recent work has shown that the RG scheme for the dimer model could be ``discovered'' by a neural network attempting to solve an IB-like problem. This manuscript explores whether IB and any existing formulation of RG are formally equivalent. A class of soft-cutoff non-perturbative RG techniques are defined by families of non-deterministic coarsening maps, and hence can be formally mapped onto IB, and vice versa. For concreteness, this discussion is limited entirely to Gaussian statistics (GIB), for which IB has exact, closed-form solutions. Under this constraint, GIB has a semigroup structure, in which successive transformations remain IB-optimal. Further, the RG cutoff scheme associated with GIB can be identified. Our results suggest that IB can be used to impose a notion of ``large scale'' structure, such as biological function, on an RG procedure.

DENSITY-MATRIX RENORMALISATION GROUP FOR DYNAMIC CORRELATION FUNCTIONS

2003 ◽  
Vol 17 (28) ◽  
pp. 5453-5457
Author(s):  
E. JECKELMANN
Keyword(s):  
Density Matrix ◽  
Variational Problem ◽  
Correlation Functions ◽  
Renormalisation Group ◽  
Many Body ◽  
Dynamic Correlation ◽  
Many Body Systems ◽  
The One ◽  
Low Dimensional ◽  
Insulating Phase

The calculation of dynamic correlation functions in quantum systems is formulated as a variational problem. For low-dimensional many-body systems this variational problem can be solved numerically using the density-matrix renormalisation group (DMRG). This dynamic DMRG method is demonstrated on the linear optical conductivity in the Mott insulating phase of the one-dimensional extended Hubbard model at half filling. The full optical spectrum of this model can be calculated almost exactly for chains with more than 100 sites, which is large enough to investigate the spectral properties in the thermodynamic limit. The accuracy of the method is illustrated by comparison with analytical results in the field-theoretical regime and in the strong-coupling limit.

scholarly journals Selected applications of typicality to real-time dynamics of quantum many-body systems

2020 ◽  
Vol 75 (5) ◽  
pp. 421-432 ◽  
Author(s):  
Tjark Heitmann ◽  
Jonas Richter ◽  
Dennis Schubert ◽  
Robin Steinigeweg
Keyword(s):  
Gibbs State ◽  
Transport Coefficients ◽  
Linear Response Theory ◽  
Numerical Approach ◽  
Many Body ◽  
Lattice Systems ◽  
Initial State ◽  
Time Dynamics ◽  
Many Body Systems ◽  
Low Dimensional

AbstractLoosely speaking, the concept of quantum typicality refers to the fact that a single pure state can imitate the full statistical ensemble. This fact has given rise to a rather simple but remarkably useful numerical approach to simulate the dynamics of quantum many-body systems, called dynamical quantum typicality (DQT). In this paper, we give a brief overview of selected applications of DQT, where particular emphasis is given to questions on transport and thermalization in low-dimensional lattice systems like chains or ladders of interacting spins or fermions. For these systems, we discuss that DQT provides an efficient means to obtain time-dependent equilibrium correlation functions for comparatively large Hilbert-space dimensions and long time scales, allowing the quantitative extraction of transport coefficients within the framework of, e. g., linear response theory (LRT). Furthermore, it is discussed that DQT can also be used to study the far-from-equilibrium dynamics resulting from sudden quench scenarios, where the initial state is a thermal Gibbs state of the pre-quench Hamiltonian. Eventually, we summarize a few combinations of DQT with other approaches such as numerical linked cluster expansions or projection operator techniques. In this way, we demonstrate the versatility of DQT.

scholarly journals The importance of being integrable: Out of the paper, into the lab

2014 ◽  
Vol 28 (18) ◽  
pp. 1430010 ◽  
Author(s):  
Murray T. Batchelor
Keyword(s):  
Quantum Physics ◽  
Three Dimensional ◽  
Integrable Model ◽  
Theoretical Physics ◽  
Many Body ◽  
One Dimensional ◽  
S Matrix ◽  
Many Body Systems ◽  
Low Dimensional ◽  
Traditional Setting

The scattering matrix (S-matrix), relating the initial and final states of a physical system undergoing a scattering process, is a fundamental object in quantum mechanics and quantum field theory. The study of factorized S-matrices, in which many-body scattering factorizes into a product of two-body terms to yield an integrable model, has long been considered the domain of mathematical physics. Many beautiful results have been obtained over several decades for integrable models of this kind, with far reaching implications in both mathematics and theoretical physics. The viewpoint that these were only toy models changed dramatically with brilliant experimental advances in realizing low-dimensional quantum many-body systems in the lab. These recent experiments involve both the traditional setting of condensed matter physics and the trapping and cooling of atoms in optical lattices to engineer and study quasi-one-dimensional systems. In some cases the quantum physics of one-dimensional systems is arguably more interesting than their three-dimensional counterparts, because the effect of interactions is more pronounced when atoms are confined to one dimension. This article provides a brief overview of these ongoing developments, which highlight the fundamental importance of integrability.

scholarly journals Spectral gap optimization of order parameters for sampling complex molecular systems

2016 ◽  
Vol 113 (11) ◽  
pp. 2839-2844 ◽  
Author(s):  
Pratyush Tiwary ◽  
B. J. Berne
Keyword(s):  
Spectral Gap ◽  
Umbrella Sampling ◽  
Order Parameters ◽  
Enhanced Sampling ◽  
Many Body ◽  
Collective Variables ◽  
Molecular Systems ◽  
Many Body Systems ◽  
Entropy Estimate ◽  
Low Dimensional

In modern-day simulations of many-body systems, much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CVs) or reaction coordinates. A vast array of enhanced-sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here, we describe a new algorithm for finding optimal low-dimensional CVs for use in enhanced-sampling biasing methods like umbrella sampling, metadynamics, and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. The algorithm is called spectral gap optimization of order parameters (SGOOP). Through multiple practical examples, we show how this postprocessing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs.

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