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C. H. Mak

Publications and source records attributed to C. H. Mak.

At least 19 recordsLinked to original sources
arXiv2007

A New Monte Carlo Method and Its Implications for Generalized Cluster Algorithms

We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of cluster-type Monte Carlo methods, and the generalization makes it possible to derive cluster algorithms for systems with both discrete and continuous degrees of freedom. The roughening transition in the sine-Gordon model has been studied with this method, and high-accuracy simulations for system sizes up to $1024^2$ were carried out to examine the logarithmic divergence of the surface roughness above the transition temperature, revealing clear evidence for universal scaling of the Kosterlitz-Thouless type.

cond-mat.soft↗
arXiv2006

Stochastic Potential Switching Algorithm for Monte Carlo Simulations of Complex Systems

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential $V$ to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential $\tilde V$. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential $V$. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude.

cond-mat.stat-mech↗
arXiv2005

Large-Scale Simulations of the Two-Dimensional Melting of Hard Disks

Large-scale computer simulations involving more than a million particles have been performed to study the melting transition in a two-dimensional hard disk fluid. The van der Waals loop previously observed in the pressure-density relationship of smaller simulations is shown to be an artifact of finite-size effects. Together with a detailed scaling analysis of the bond orientation order, the new results provide compelling evidence for the Halperin-Nelson-Young picture. Scaling analysis of the translational order also yields a lower bound for the melting density that is much higher than previously thought.

cond-mat.soft↗
arXiv2004

A Multigrid Algorithm for Sampling Imaginary-Time Paths in Quantum Monte Carlo Simulations

We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid method to rapidly accelerate the sampling of paths in a quantum Monte Carlo simulation, making its dynamics more ergodic. The effectiveness and efficiency of this method are demonstrated for several one-dimensional quantum systems and compared to other standard and accelerated methods.

cond-mat.stat-mech↗
arXiv2001

Relieving the fermionic and the dynamical sign problem: Multilevel Blocking Monte Carlo simulations

This article gives an introduction to the multilevel blocking (MLB) approach to both the fermion and the dynamical sign problem in path-integral Monte Carlo simulations. MLB is able to substantially relieve the sign problem in many situations. Besides an exposition of the method, its accuracy and several potential pitfalls are discussed, providing guidelines for the proper choice of certain MLB parameters. Simulation results are shown for strongly interacting electrons in a 2D parabolic quantum dot, the real-time dynamics of several simple model systems, and the dissipative two-state dynamics (spin-boson problem).

cond-mat.stat-mech↗
arXiv1999

Multilevel blocking Monte Carlo simulations for quantum dots

This article provides an introduction to the ideas behind the multilevel blocking (MLB) approach to the fermion sign problem in path-integral Monte Carlo simulations, and also gives a detailed discussion of MLB results for quantum dots. MLB can turn the exponential severity of the sign problem into an algebraic one, thereby enabling numerically exact studies of otherwise inaccessible systems. Low-temperature simulation results for up to eight strongly correlated electrons in a parabolic 2D quantum dot are presented.

cond-mat.str-el↗
arXiv1999

Crossover from Fermi liquid to Wigner molecule behavior in quantum dots

The crossover from weak to strong correlations in parabolic quantum dots at zero magnetic field is studied by numerically exact path-integral Monte Carlo simulations for up to eight electrons. By the use of a multilevel blocking algorithm, the simulations are carried out free of the fermion sign problem. We obtain a universal crossover only governed by the density parameter $r_s$. For $r_s>r_c$, the data are consistent with a Wigner molecule description, while for $r_s<r_c$, Fermi liquid behavior is recovered. The crossover value $r_c \approx 4$ is surprisingly small.

cond-mat.str-el↗
arXiv1998

A Stochastic Liouvillian Algorithm to Simulate Dissipative Quantum Dynamics With Arbitrary Precision

An exact and efficient new method to simulate dynamics in dissipative quantum systems is presented. A stochastic Liouville equation, deduced from Feynman and Vernon's path-integral expression of the reduced density matrix, is used to describe the exact dynamics at any dissipative strength and for arbitrarily low temperatures. The utility of the method is demonstrated by applications to a damped harmonic oscillator and a double-well system immersed in an Ohmic bath at low temperatures.

cond-mat.stat-mech↗
arXiv1998

Inter- and Intra-Chain Attractions in Solutions of Flexible Polyelectrolytes at Nonzero Concentration

Constant temperature molecular dynamics simulations were used to study solutions of flexible polyelectrolyte chains at nonzero concentrations with explicit counterions and unscreened coulombic interactions. Counterion condensation, measured via the self-diffusion coefficient of the counterions, is found to increase with polymer concentration, but contrary to the prediction of Manning theory, the renormalized charge fraction on the chains decreases with increasing Bjerrum length without showing any saturation. Scaling analysis of the radius of gyration shows that the chains are extended at low polymer concentrations and small Bjerrum lengths, while at sufficiently large Bjerrum lengths, the chains shrink to produce compact structures with exponents smaller than a gaussian chain, suggesting the presence of attractive intrachain interactions. A careful study of the radial distribution function of the center-of-mass of the polyelectrolyte chains shows clear evidence that effective interchain attractive interactions also exist in solutions of flexible polyelectrolytes, similar to what has been found for rodlike polyelectrolytes. Our results suggest that the broad maximum observed in scattering experiments is due to clustering of chains.

cond-mat.stat-mech↗
arXiv1998

A Multilevel Blocking Approach to the Sign Problem in Real-Time Quantum Monte Carlo Simulations

We propose a novel approach toward the general solution of the sign problem in real-time path-integral simulations. Using a recursive multilevel blocking strategy, this method circumvents the sign problem by synthesizing the phase cancellations arising from interfering quantum paths on multiple timescales. A number of numerical examples with one or a few explicit degrees of freedom illustrate the usefulness of the method.

physics.chem-ph↗
arXiv1998

Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations

A general algorithm toward the solution of the fermion sign problem in finite-temperature quantum Monte Carlo simulations has been formulated for discretized fermion path integrals with nearest-neighbor interactions in the Trotter direction. This multilevel approach systematically implements a simple blocking strategy in a recursive manner to synthesize the sign cancellations among different fermionic paths throughout the whole configuration space. The practical usefulness of the method is demonstrated for interacting electrons in a quantum dot.

cond-mat.stat-mech↗
arXiv1998

Stabilizing dynamical localization in driven tunneling

Dynamical localization of a tunneling system by means of an oscillating external field is examined for an arbitrary doublet of tunneling states. We show that the condition of an exact crossing of Floquet levels, required for localization in a symmetric system, can be substantially relaxed for tunneling systems with broken symmetry. This generalization equally applies to tunneling systems coupled to a dissipative environment.

cond-mat↗
arXiv1998

Dynamical simulation of current fluctuations in a dissipative two-state system

Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over the real-time paths under the influence of colored noise. The nature of the transition from coherent to incoherent dynamics at low temperatures is re-examined.

cond-mat.stat-mech↗
arXiv1997

Is the direct observation of electronic coherence in electron transfer reactions possible?

The observability of electronic coherence in electron transfer reactions is discussed. We show that under appropriate circumstances large-amplitude oscillations can be found in the electronic occupation probabilities. The initial preparation of the system is of crucial importance for this effect, and we discuss conditions under which experiments detecting electronic coherence should be feasible. The Feynman-Vernon influence functional formalism is extended to examine more general and experimentally relevant initial preparations. Analytical expressions and path integral quantum dynamics simulations were developed to study the effects of various initial preparations on the observability of electronic coherence.

cond-mat↗
arXiv1996

A Dynamical Theory of Electron Transfer: Crossover from Weak to Strong Electronic Coupling

We present a real-time path integral theory for the rate of electron transfer reactions. Using graph theoretic techniques, the dynamics is expressed in a formally exact way as a set of integral equations. With a simple approximation for the self-energy, the rate can then be computed analytically to all orders in the electronic coupling matrix element. We present results for the crossover region between weak (nonadiabatic) and strong (adiabatic) electronic coupling and show that this theory provides a rigorous justification for the salient features of the rate expected within conventional electron transfer theory. Nonetheless, we find distinct characteristics of quantum behavior even in the strongly adiabatic limit where classical rate theory is conventionally thought to be applicable. To our knowledge, this theory is the first systematic dynamical treatment of the full crossover region.

chem-ph↗
arXiv1995

Dynamical simulation of transport in one-dimensional quantum wires

Transport of single-channel spinless interacting fermions (Luttinger liquid) through a barrier has been studied by numerically exact quantum Monte Carlo methods. A novel stochastic integration over the real-time paths allows for direct computation of nonequilibrium conductance and noise properties. We have examined the low-temperature scaling of the conductance in the crossover region between a very weak and an almost insulating barrier.

cond-mat↗
arXiv1994

Low-temperature dynamical simulation of spin-boson systems

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.

chem-ph↗