scholarly journals Critical non-Hermitian skin effect

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Linhu Li ◽  
Ching Hua Lee ◽  
Sen Mu ◽  
Jiangbin Gong
Keyword(s):  
Thermodynamic Limit ◽  
Skin Effect ◽  
Finite Size ◽  
System Size ◽  
Critical Systems ◽  
Anomalous Scaling ◽  
Lattice Systems ◽  
New Class ◽  
Rlc Circuit ◽  
Zero Coupling

Abstract Critical systems represent physical boundaries between different phases of matter and have been intensely studied for their universality and rich physics. Yet, with the rise of non-Hermitian studies, fundamental concepts underpinning critical systems - like band gaps and locality - are increasingly called into question. This work uncovers a new class of criticality where eigenenergies and eigenstates of non-Hermitian lattice systems jump discontinuously across a critical point in the thermodynamic limit, unlike established critical scenarios with spectrum remaining continuous across a transition. Such critical behavior, dubbed the “critical non-Hermitian skin effect”, arises whenever subsystems with dissimilar non-reciprocal accumulations are coupled, however weakly. This indicates, as elaborated with the generalized Brillouin zone approach, that the thermodynamic and zero-coupling limits are not exchangeable, and that even a large system can be qualitatively different from its thermodynamic limit. Examples with anomalous scaling behavior are presented as manifestations of the critical non-Hermitian skin effect in finite-size systems. More spectacularly, topological in-gap modes can even be induced by changing the system size. We provide an explicit proposal for detecting the critical non-Hermitian skin effect in an RLC circuit setup, which also directly carries over to established setups in non-Hermitian optics and mechanics.

scholarly journals THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

2004 ◽  
Vol 15 (09) ◽  
pp. 1249-1268 ◽  
Author(s):  
DENIS HORVÁTH ◽  
MARTIN GMITRA
Keyword(s):  
Monte Carlo ◽  
Finite Size ◽  
Simulation Method ◽  
Monte Carlo Step ◽  
The Self ◽  
Square Lattice ◽  
Critical Systems ◽  
Lattice Systems ◽  
Steady Regime ◽  
Self Organized

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

scholarly journals Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Alexander McDonald ◽  
Aashish A. Clerk
Keyword(s):  
Skin Effect ◽  
Tight Binding ◽  
Quantum Fisher Information ◽  
System Size ◽  
Distinct Advantage ◽  
Lattice Systems ◽  
Spatially Extended ◽  
Potential Applications ◽  
Spatially Extended Systems ◽  
Quantum Optical

Abstract Non-Hermitian systems exhibit markedly different phenomena than their conventional Hermitian counterparts. Several such features, such as the non-Hermitian skin effect, are only present in spatially extended systems. Potential applications of these effects in many-mode systems however remains largely unexplored. Here, we study how unique features of non-Hermitian lattice systems can be harnessed to improve Hamiltonian parameter estimation in a fully quantum setting. While the quintessential non-Hermitian skin effect does not provide any distinct advantage, alternate effects yield dramatic enhancements. We show that certain asymmetric non-Hermitian tight-binding models with a $${{\mathbb{Z}}}_{2}$$ Z 2 symmetry yield a pronounced sensing advantage: the quantum Fisher information per photon increases exponentially with system size. We find that these advantages persist in regimes where non-Markovian and non-perturbative effects become important. Our setup is directly compatible with a variety of quantum optical and superconducting circuit platforms, and already yields strong enhancements with as few as three lattice sites.

scholarly journals Kirkwood-Buff Integrals Using Molecular Simulation: Estimation of Surface Effects

Nanomaterials ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 771 ◽  
Author(s):  
Noura Dawass ◽  
Peter Krüger ◽  
Sondre K. Schnell ◽  
Othonas A. Moultos ◽  
Ioannis G. Economou ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Thermodynamic Limit ◽  
Finite Size ◽  
Surface Effects ◽  
System Size ◽  
Distribution Functions ◽  
Finite Systems ◽  
System Method ◽  
The One ◽  
The Relationship

Kirkwood-Buff (KB) integrals provide a connection between microscopic properties and thermodynamic properties of multicomponent fluids. The estimation of KB integrals using molecular simulations of finite systems requires accounting for finite size effects. In the small system method, properties of finite subvolumes with different sizes embedded in a larger volume can be used to extrapolate to macroscopic thermodynamic properties. KB integrals computed from small subvolumes scale with the inverse size of the system. This scaling was used to find KB integrals in the thermodynamic limit. To reduce numerical inaccuracies that arise from this extrapolation, alternative approaches were considered in this work. Three methods for computing KB integrals in the thermodynamic limit from information of radial distribution functions (RDFs) of finite systems were compared. These methods allowed for the computation of surface effects. KB integrals and surface terms in the thermodynamic limit were computed for Lennard–Jones (LJ) and Weeks–Chandler–Andersen (WCA) fluids. It was found that all three methods converge to the same value. The main differentiating factor was the speed of convergence with system size L. The method that required the smallest size was the one which exploited the scaling of the finite volume KB integral multiplied by L. The relationship between KB integrals and surface effects was studied for a range of densities.

scholarly journals Beyond the thermodynamic limit: finite-size corrections to state interconversion rates

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 108 ◽  
Author(s):  
Christopher T. Chubb ◽  
Marco Tomamichel ◽  
Kamil Korzekwa
Keyword(s):  
Thermodynamic Limit ◽  
Size Effects ◽  
Heat Engine ◽  
Finite Size ◽  
Average Energy ◽  
System Size ◽  
Mathematical Framework ◽  
Single Shot ◽  
Final State ◽  
Finite Size Effects

Thermodynamics is traditionally constrained to the study of macroscopic systems whose energy fluctuations are negligible compared to their average energy. Here, we push beyond this thermodynamic limit by developing a mathematical framework to rigorously address the problem of thermodynamic transformations of finite-size systems. More formally, we analyse state interconversion under thermal operations and between arbitrary energy-incoherent states. We find precise relations between the optimal rate at which interconversion can take place and the desired infidelity of the final state when the system size is sufficiently large. These so-called second-order asymptotics provide a bridge between the extreme cases of single-shot thermodynamics and the asymptotic limit of infinitely large systems. We illustrate the utility of our results with several examples. We first show how thermodynamic cycles are affected by irreversibility due to finite-size effects. We then provide a precise expression for the gap between the distillable work and work of formation that opens away from the thermodynamic limit. Finally, we explain how the performance of a heat engine gets affected when one of the heat baths it operates between is finite. We find that while perfect work cannot generally be extracted at Carnot efficiency, there are conditions under which these finite-size effects vanish. In deriving our results we also clarify relations between different notions of approximate majorisation.

Transfer Matrix Study of Finite-size Corrections in the 2D Ising Model

2005 ◽  
Vol 5 (1) ◽  
pp. 72-85 ◽  
Author(s):  
J. Kaupužs
Keyword(s):  
Correlation Function ◽  
Ising Model ◽  
Transfer Matrix ◽  
Finite Size ◽  
Lattice Systems ◽  
Small Magnitude ◽  
Amplitude Correction ◽  
Matrix Algorithms ◽  
Point Correlation ◽  
Point Correlation Function

AbstractEffective exact transfer matrix algorithms have been developed to compute the two-point correlation function G(r) of the 2D Ising model on a square finite size lattice. Systems including up to 800 spins have been considered and corrections to the finite-size scaling at the critical point have been analysed.As a new result, we have found that the correlation function has a nontrivial amplitude correction of a very small magnitude.

scholarly journals Finite-size behaviour of a critical related observable

Open Physics ◽  
2012 ◽  
Vol 10 (6) ◽  
Author(s):  
Wu Yuanfang ◽  
Chen Lizhu ◽  
Pan Xue ◽  
Shao Ming ◽  
Xiaosong Chen
Keyword(s):  
Fixed Point ◽  
Heavy Ion Collisions ◽  
Finite Size ◽  
System Size ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Charge Fluctuations ◽  
Qcd Critical Point ◽  
Ion Collisions ◽  
Straight Line

AbstractAccounting for the influence of system size in relativistic heavy ion collisions, the finite-size form of a critical related observable is suggested. The fixed-point and straight line methods are proposed in exploring the QCD critical point and phase boundary in relativistic heavy ion collisions. As an application, the finitesize behaviour of the ratios of higher net-proton cumulants, dynamical electric charge fluctuations, and transverse momentum correlations in Au + Au collisions at RHIC are examined.

Voltage Response of ZnO Varistors to 8/20 µs Surge Current

2007 ◽  
Vol 280-283 ◽  
pp. 285-288 ◽  
Author(s):  
Zhen Ya Lu ◽  
Zhi Wu Chen ◽  
Feng Jin Yang
Keyword(s):  
Skin Effect ◽  
Voltage Response ◽  
Voltage Waveform ◽  
Residual Voltage ◽  
Zno Varistor ◽  
Rlc Circuit ◽  
Rear Part ◽  
Zno Varistors ◽  
Voltage Peak ◽  
Surge Current

The voltage response of ZnO varistors to 8/20 µs surge current was investigated. The observed frontal spikes on the residual voltage waveforms are caused by the ignition gap, and no frontal spike was observed when a thyristor was used as the discharge trigger. The rear part of the waveform is determined by the damping coefficient of the RLC-circuit. Near the critical point, the residual voltage waveform changes from non-oscillating attenuation modes to distinct across zero oscillating modes along with the increase of the peak current, but there will be no oscillation happen when a thyristor is used as the discharge trigger. The residual voltage peak is not synchronized with the current peak, and the voltage peak is leading, implying that the ZnO varistor appears to be inductive. According to the experiment results, it can be reasonably explained that the voltage peak leading phenomenon is attributed to the transient skin effect of the varistor materials.

MONTE CARLO STUDY OF ONE HOLE IN A QUANTUM ANTIFERROMAGNET

1992 ◽  
Vol 06 (05n06) ◽  
pp. 587-588
Author(s):  
S. Sorella
Keyword(s):  
Magnetic Field ◽  
Monte Carlo ◽  
Thermodynamic Limit ◽  
Quantum Monte Carlo ◽  
Finite Size ◽  
Monte Carlo Study ◽  
Mott Insulator ◽  
Trial Wavefunction ◽  
The One ◽  
Quantum Antiferromagnet

Using the standard Quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a Quantum Antiferromagnet. The calculation is very well stabilized, using selected sized systems and special use of the trial wavefunction that satisfy the “close shell condition” in presence of an arbitrarily weak Zeeman magnetic field, vanishing in the thermodynamic limit. It will be shown in a forthcoming publication1 that the presence of this magnetic field does not affect thermodynamic properties for the half filled system. Then I have used the same selected sizes for the one hole ground state. I have investigated the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator should behave just as conventional insulator with an upper and lower Hubbard band. By comparing the present finite size scaling with several techniques predicting a finite quasiparticle weight (see Fig.1) the data seem more consistent with a vanishing quasiparticle weight, i.e. , as recently suggested by P.W. Anderson2 the Hubbard-Mott insulator should be characterized by non-trivial excitations which cannot be interpreted in a simple quasi-particle picture. However it cannot be excluded , based only on numerical grounds, that a very small but non vanishing quasiparticle weight should survive in the thermodynamic limit.

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