arXiv subjects

Omri Gat

Publications and source records attributed to Omri Gat.

48 records · Page 3Linked to original sources

arXiv2004

Formation and annihilation of laser light pulse quanta in thermodynamic-like pathway

We present a theoretical and experimental study of multiple pulse formation in passively mode-locked (PML) lasers. Following a statistical mechanics approach, the study yields a thermodynamic-like "phase diagram" with boundaries representing cascaded first order phase transitions. They correspond to abrupt creation or annihilation of pulses and a quantized RF power behavior, as system parameters (noise and/or pumping levels) are varied, in excellent accordance with the experiments. Remarkably, individual pulses carry an almost constant quantum of energy.

cond-mat.stat-mech↗

arXiv2004

Exact solution of the nonlinear laser passive mode locking transition

We present the first statistical mechanics study of a passively mode locked laser which includes all the main physical processes, saturable absorption, Kerr nonlinearity, parabolic gain filtering and group velocity dispersion, assuming the soliton condition. We achieve an exact solution in the thermodynamic limit, where the ratio of the cavity length to the pulse width, the duty cycle, tends to infinity. The thermodynamics depends on a single dimensionless parameter $γ$, the ratio of the correlation length to the pulse width. The phase diagram consists of one ordered, mode-locked phase and one disordered, continuous wave phase, separated by a first order phase transition at $γ=9$. The model belongs to a new class of solvable statistical mechanics models with a non-trivial phase diagram. The results are obtained with a fully controlled transfer matrix calculation, showing rigorously that passive mode locking is a thermodynamic phase transition.

cond-mat.stat-mech↗

arXiv2003

Solution of a statistical mechanics model for pulse formation in lasers

We present a rigorous statistical-mechanics theory of nonlinear many mode laser systems. An important example is the passively mode-locked laser that promotes pulse operation when a saturable absorber is placed in the cavity. It was shown by Gordon and Fischer [1] that pulse formation is a first-order phase transition of spontaneous ordering of modes in an effective "thermodynamic" system, in which intracavity noise level is the effective temperature. In this paper we present a rigorous solution of a model of passive mode locking. We show that the thermodynamics depends on a single parameter, and calculate exactly the mode-locking point. We find the phase diagram and calculate statistical quantities, including the dependence of the intracavity power on the gain saturation function, and finite size corrections near the transition point. We show that the thermodynamics is independent of the gain saturation mechanism and that it is correctly reproduced by a mean field calculation. The outcome is a new solvable statistical mechanics system with an unstable self-interaction accompanied by a natural global power constraint, and an exact description of an important many mode laser system.

cond-mat.stat-mech↗

arXiv1999

Transport properties and phase diagram of the disordered lattice vibration model

We study the transport and localization properties of scalar vibrations on a lattice with random bond strength by means of the transfer matrix method. This model has been recently suggested as a means to investigate the vibrations and heat conduction properties of structural glasses. In three dimensions we find a very rich phase diagram. The delocalization transition is split, so that between the localized and diffusive phases which have been identified in the Anderson problem, we observe a phase with anomalous, sub-exponential localization. For low frequencies, we find a strongly conducting phase with ballistic and super-diffusive transport, reflecting a diverging diffusivity. The last phase generates an anomalous heat conductivity which grows with the system size. These phases are the counterparts of those identified in an earlier study of the normal modes.

cond-mat.dis-nn↗

arXiv1999

Hydrodynamic Lyapunov Modes in Translation Invariant Systems

We study the implications of translation invariance on the tangent dynamics of extended dynamical systems, within a random matrix approximation. In a model system, we show the existence of hydrodynamic modes in the slowly growing part of the Lyapunov spectrum, which are analogous to the hydrodynamic modes discovered numerically by [Dellago, Ch., Posch, H.A., Hoover, W.G., Phys. Rev. E 53, 1485 (1996)]. The hydrodynamic Lyapunov vectors loose the typical random structure and exhibit instead the structure of weakly perturbed coherent long wavelength waves. We show further that the amplitude of the perturbations vanishes in the thermodynamic limit, and that the associated Lyapunov exponents are universal.

chao-dyn↗

arXiv1998

Anomalous scaling in passive scalar advection: Monte-Carlo Lagrangian trajectories

We present a numerical method which is used to calculate anomalous scaling exponents of structure functions in the Kraichnan passive scalar advection model (R. H. Kraichnan, Phys. Fluids {\bf11}, 945 (1968)). This Monte-Carlo method, which is applicable in any space dimension, is based on the Lagrangian path interpretation of passive scalar dynamics, and uses the recently discovered equivalence between scaling exponents of structure functions and relaxation rates in the stochastic shape dynamics of groups of Lagrangian particles. We calculate third and fourth order anomalous exponents for several dimensions, comparing with the predictions of perturbative calculations in large dimensions. We find that Kraichnan's closure appears to give results in close agreement with the numerics. The third order exponents are compatible with our own previous nonperturbative calculations.

cond-mat.stat-mech↗

arXiv1997

Multiscaling in passive scalar advection as stochastic shape dynamics

The Kraichnan rapid advection model is recast as the stochastic dynamics of tracer trajectories. This framework replaces the random fields with a small set of stochastic ordinary differential equations. Multiscaling of correlation functions arises naturally as a consequence of the geometry described by the evolution of N trajectories. Scaling exponents and scaling structures are interpreted as excited states of the evolution operator. The trajectories become nearly deterministic in high dimensions allowing for perturbation theory in this limit. We calculate perturbatively the anomalous exponent of the third and fourth order correlation functions. The fourth order result agrees with previous calculations.

cond-mat.stat-mech↗

arXiv1997

Invading interfaces and blocking surfaces in high dimensional disordered systems

We study the high-dimensional properties of an invading front in a disordered medium with random pinning forces. We concentrate on interfaces described by bounded slope models belonging to the quenched KPZ universality class. We find a number of qualitative transitions in the behavior of the invasion process as dimensionality increases. In low dimensions $d<6$ the system is characterized by two different roughness exponents, the roughness of individual avalanches and the overall interface roughness. We use the similarity of the dynamics of an avalanche with the dynamics of invasion percolation to show that above $d=6$ avalanches become flat and the invasion is well described as an annealed process with correlated noise. In fact, for $d\geq5$ the overall roughness is the same as the annealed roughness. In very large dimensions, strong fluctuations begin to dominate the size distribution of avalanches, and this phenomenon is studied on the Cayley tree, which serves as an infinite dimensional limit. We present numerical simulations in which we measured the values of the critical exponents of the depinning transition, both in finite dimensional lattices with $d\leq6$ and on the Cayley tree, which support our qualitative predictions. We find that the critical exponents in $d=6$ are very close to their values on the Cayley tree, and we conjecture on this basis the existence of a further dimension, where mean field behavior is obtained.

cond-mat.stat-mech↗

arXiv1997

Perturbative and Non-Perturbative Analysis of the 3'rd Order Zero Modes

The anomalous scaling behavior of the n-th order correlation functions $F_n$ of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero-modes) of the Kraichnan equation $\hat{B}_n F_n=0$. In this paper we present an extensive analysis of the simplest (non-trivial) case of n=3 in the isotropic sector. The main parameter of the model, denoted as $ζ_h$, characterizes the eddy diffusivity and can take values in the interval $0\le ζ_h \le 2$. After choosing appropriate variables we can present computer-assisted non-perturbative calculations of the zero modes in a projective two dimensional circle. In this presentation it is also very easy to perform perturbative calculations of the scaling exponent $ζ_3$ of the zero modes in the limit $ζ_h\to 0$, and we display quantitative agreement with the non-perturbative calculations in this limit. Another interesting limit is $ζ_h\to 2$. This second limit is singular, and calls for a study of a boundary layer using techniques of singular perturbation theory. Our analysis of this limit shows that the scaling exponent $ζ_3$ vanishes like $\sqrt{ζ_2/log{ζ_2}}$. In this limit as well, perturbative calculations are consistent with the non-perturbative calculations.

chao-dyn↗

arXiv1996

Non-Perturbative Zero Modes in the Kraichnan Model for Turbulent Advection

The anomalous scaling behavior of the n-th order correlation functions ${\cal F}_n$ of the Kraichnan model of turbulent passive scalar advection is believed to be dominated by the homogeneous solutions (zero-modes) of the Kraichnan equation $\hat{\cal B}_n {\cal F}_n=0$. Previous analysis found zero-modes in perturbation theory in a small parameter. We present non-perturbative analysis of the simplest (non-trivial) case of n=3 and compare the results with the perturbative predictions.

chao-dyn↗

arXiv1996

High dimensional properties of quenched noise growth models

We discuss the behavior of bounded slope quenched noise invasion models in high dimensions. We first observe that the roughness of such a steady state interface is generated by the combination of the roughness of the invasion process $χ_c$ and the roughness of the underlying interface dynamics. In high enough dimension we argue that $χ_c$ decreases to zero. This defines a critical dimension for the problem, over which it reduces to the correlated annealed dynamics, which we show to have the same roughness as the annealed equation at five dimensions. We argue that on the Cayley tree with one additional height coordinate the associated processes are fractal. The critical behavior is anomalous due to strong effects of rare events. Numerical simulations of the model on a Cayley tree and high dimensional lattices support those theoretical predictions.

cond-mat↗

arXiv1994

The Breakdown of Dynamic Scaling and Intermittency in a Cascade Model of Turbulence

We present an analytic and numerical analysis of the Gledzer-Ohkitani-Yamada (GOY) cascade model for turbulence. We concentrate on the dynamic correlations, and demonstrate both numerically and analytically, using resummed perturbation theory, that the correlations do not follow a dynamic scaling ansatz. The basic reason for this is the existence of a second quadratic invariant, in addition to energy. This implies the breakdown of the Kolmogorov type scaling law, in a manner different from the conventional mechanisms proposed for Navier-Stokes intermittency. By modifying the model equation so as to eliminate the spurious invariant, we recover to good accuracy, both dynamic scaling and the Kolmogorov exponents. We conclude that intermittency in the GOY model may be attributed to the effects of the spurious invariant which does not exist in the 3-dimensional Navier-Stokes flow.

chao-dyn↗