arXiv subjects

V. Freilikher

Publications and source records attributed to V. Freilikher.

At least 19 recordsLinked to original sources

arXiv2010

Bistability of Anderson localized states in nonlinear random media

We study wave transmission through one-dimensional random nonlinear structures and predict a novel effect resulting from an interplay of nonlinearity and disorder. We reveal that, while weak nonlinearity does not change the typical exponentially small transmission in the regime of the Anderson localization, it affects dramatically the disorder-induced localized states excited inside the medium leading to {\em bistable} and {\em nonreciprocal} resonant transmission. Our numerical modelling shows an excellent agreement with theoretical predictions based on the concept of a high-Q resonator associated with each localized state. This offers a new way of all-optical light control employing statistically-homogeneous random media without regular cavities.

physics.optics↗

arXiv2008

Coupling and Level Repulsion in the Localized Regime: From Isolated to Quasi-Extended Modes

We study the interaction of Anderson localized states in an open 1D random system by varying the internal structure of the sample. As the frequencies of two states come close, they are transformed into multiply-peaked quasi-extended modes. Level repulsion is observed experimentally and explained within a model of coupled resonators. The spectral and spatial evolution of the coupled modes is described in terms of the coupling coefficient and Q-factors of resonators.

cond-mat.dis-nn↗

arXiv2006

Localized Modes in Open One-Dimensional Dissipative Random Systems

We consider, both theoretically and experimentally, the excitation and detection of the localized quasi-modes (resonances) in an open dissipative 1D random system. We show that even though the amplitude of transmission drops dramatically so that it cannot be observed in the presence of small losses, resonances are still clearly exhibited in reflection. Surprisingly, small losses essentially improve conditions for the detection of resonances in reflection as compared with the lossless case. An algorithm is proposed and tested to retrieve sample parameters and resonances characteristics inside the random system exclusively from reflection measurements.

cond-mat.dis-nn↗

arXiv2005

Effect of spatial-time dispersion on the propagation of electromagnetic waves in photonic crystals

We study the influence of the space and time dispersion on the frequency dependence of the wave vectors of electromagnetic waves propagating in three-dimensional photonic crystals. Two types of structures are considered: media with weak periodic modulation of the permittivity, and photonic crystals composed of the periodically arranged identical resonant dielectric particles. It is shown that in these systems, in contrast to electrons in solid crystals, different types of excitations exist. For example, a peculiar kind of polaritons arises in the photonic crystals due to the interaction of the electromagnetic field, eigenoscillations of the dielectric medium, and Debye resonance. The widths of the transparency zones and of the band gaps have been calculated as functions of the frequency and of the parameters of the media. It is shown that in the photonic crystals with dispersion, the number of transparency bands is larger than in non-dispersive systems, and the width of the gaps in the frequency spectrum of photons depends on the wave vector. The interaction of different types of waves deforms the Brillouin zone, so that it may not have a plane boundary (for example, a sphere), in which case the classical Bragg condition does not hold.

cond-mat.other↗

arXiv2003

Resonances in 1D disordered systems: localization of energy and resonant transmission

Localized states in one-dimensional open disordered systems and their connection to the internal structure of random samples have been studied. It is shown that the localization of energy and anomalously high transmission associated with these states are due to the existence inside the sample of a transparent (for a given resonant frequency) segment with the minimal size of order of the localization length. A mapping of the stochastic scattering problem in hand onto a deterministic quantum problem is developed. It is shown that there is no one-to-one correspondence between the localization and high transparency: only small part of localized modes provides the transmission coefficient close to one. The maximal transmission is provided by the modes that are localized in the center, while the highest energy concentration takes place in cavities shifted towards the input. An algorithm is proposed to estimate the position of an effective resonant cavity and its pumping rate by measuring the resonant transmission coefficient. The validity of the analytical results have been checked by extensive numerical simulations and wavelet analysis.

cond-mat.dis-nn↗

arXiv2003

Local and average fields inside surface-disordered waveguides: Resonances in the one-dimensional Anderson localization regime

We investigate the one-dimensional propagation of waves in the Anderson localization regime, for a single-mode, surface disordered waveguide. We make use of both an analytical formulation and rigorous numerical simulation calculations. The occurrence of anomalously large transmission coefficients for given realizations and/or frequencies is studied, revealing huge field intensity concentration inside the disordered waveguide. The analytically predicted s-like dependence of the average intensity, being in good agreement with the numerical results for moderately long systems, fails to explain the intensity distribution observed deep in the localized regime. The average contribution to the field intensity from the resonances that are above a threshold transmission coefficient $T_{c}$ is a broad distribution with a large maximum at/near mid-waveguide, depending universally (for given $T_{c}$) on the ratio of the length of the disorder segment to the localization length, $L/ξ$. The same universality is observed in the spatial distribution of the intensity inside typical (non-resonant with respect to the transmission coefficient) realizations, presenting a s-like shape similar to that of the total average intensity for $T_{c}$ close to 1, which decays faster the lower is $T_{c}$. Evidence is given of the self-averaging nature of the random quantity $\log[I(x)]/x\simeq -1/ξ$. Higher-order moments of the intensity are also shown.

cond-mat.dis-nn↗

arXiv1999

Reflection and transmission of waves in surface-disordered waveguides

The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type disorder on the behavior of the ensemble average and fluctuations of the reflection and transmission coefficients, reflectance, transmittance, and conductance. Our results show anomalous effects stemming from the combination of mode dispersion and rough surface scattering: For a given waveguide length, the larger the mode transverse momentum is, the more strongly is the mode scattered. These effects manifest themselves in the mode selectivity of the transmission coefficients, anomalous backscattering enhancement, and speckle pattern both in reflection and transmission, reflectance and transmittance, and also in the conductance and its universal fluctuations. It is shown that, in contrast to volume impurities, surface scattering in quasi-one-dimensional structures (waveguides) gives rise to the coexistence of the ballistic, diffusive, and localized regimes within the same sample.

cond-mat.dis-nn↗

arXiv1998

Higher order parametric level statistics in disordered systems

Higher order parametric level correlations in disordered systems with broken time-reversal symmetry are studied by mapping the problem onto a model of coupled Hermitian random matrices. Closed analytical expression is derived for parametric density-density correlation function which corresponds to a perturbation of disordered system by a multicomponent flux.

cond-mat.dis-nn↗

arXiv1998

Spectra of large random matrices: A method of study

A formalism for study of spectral correlations in non-Gaussian, unitary invariant ensembles of large random matrices with strong level confinement is reviewed. It is based on the Shohat method in the theory of orthogonal polynomials. The approach presented is equally suitable for description of both local and global spectral characteristics, thereby providing an overall look at the phenomenon of spectral universality in Random Matrix Theory.

cond-mat.stat-mech↗

arXiv1997

Two-band random matrices

Spectral correlations in unitary invariant, non-Gaussian ensembles of large random matrices possessing an eigenvalue gap are studied within the framework of the orthogonal polynomial technique. Both local and global characteristics of spectra are directly reconstructed from the recurrence equation for orthogonal polynomials associated with a given random matrix ensemble. It is established that an eigenvalue gap does not affect the local eigenvalue correlations which follow the universal sine and the universal multicritical laws in the bulk and soft-edge scaling limits, respectively. By contrast, global smoothed eigenvalue correlations do reflect the presence of a gap, and are shown to satisfy a new universal law exhibiting a sharp dependence on the odd/even dimension of random matrices whose spectra are bounded. In the case of unbounded spectrum, the corresponding universal `density-density' correlator is conjectured to be generic for chaotic systems with a forbidden gap and broken time reversal symmetry.

cond-mat.stat-mech↗

arXiv1997

Random matrix models with log-singular level confinement: method of fictitious fermions

Joint distribution function of N eigenvalues of U(N) invariant random-matrix ensemble can be interpreted as a probability density to find N fictitious non-interacting fermions to be confined in a one-dimensional space. Within this picture a general formalism is developed to study the eigenvalue correlations in non-Gaussian ensembles of large random matrices possessing non-monotonic, log-singular level confinement. An effective one-particle Schroedinger equation for wave-functions of fictitious fermions is derived. It is shown that eigenvalue correlations are completely determined by the Dyson's density of states and by the parameter of the logarithmic singularity. Closed analytical expressions for the two-point kernel in the origin, bulk, and soft-edge scaling limits are deduced in a unified way, and novel universal correlations are predicted near the end point of the single spectrum support.

cond-mat↗

arXiv1997

Universality in invariant random-matrix models: Existence near the soft edge

We consider two non-Gaussian ensembles of large Hermitian random matrices with strong level confinement and show that near the soft edge of the spectrum both scaled density of states and eigenvalue correlations follow so-called Airy laws inherent in Gaussian unitary ensemble. This suggests that the invariant one-matrix models should display universal eigenvalue correlations in the soft-edge scaling limit.

chao-dyn↗

arXiv1997

Novel universal correlations in invariant random-matrix models

We show that eigenvalue correlations in unitary-invariant ensembles of large random matrices adhere to novel universal laws that only depend on a multicriticality of the bulk density of states near the soft edge of the spectrum. Our consideration is based on the previously unknown observation that genuine density of states and n-point correlation function are completely determined by the Dyson's density analytically continued onto the whole real axis.

chao-dyn↗

arXiv1996

Phase randomness in a one-dimensional disordered absorbing medium

Analytical study of the distribution of phase of the transmission coefficient through 1D disordered absorbing system is presented. The phase is shown to obey approximately Gaussian distribution. An explicit expression for the variance is obtained, which shows that absorption suppresses the fluctuations of the phase. The applicability of the random phase approximation is discussed.

cond-mat.dis-nn↗

arXiv1996

Eigenfunctions of electrons in weakly disordered quantum dots: Crossover between orthogonal and unitary symmetries

A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained with recent results derived from first principles within the framework of supersymmetry technique allows to identify a transition parameter with real microscopic characteristics of the problem. The random-matrix model is applied to the statistics of the height of the resonance conductance of a quantum dot in the regime of the crossover between orthogonal and unitary symmetry classes.

cond-mat↗

arXiv1996

Statistical Properties of the Reflectance and Transmittance of an Amplifying Random Media

Statistical properties of the transmittance ($T$) and reflectance ($R$) of an amplifying layer with one-dimensional disorder are investigated analytically. Whereas the transmittance at typical realizations decreases exponentially with the layer thickness $L$ just as it does in absorbing media, the average $\left\langle T\right\rangle $ and $\left\langle R\right\rangle $\ are shown to be infinite even for finite $L$ due to the contribution of low-probable resonant realizations corresponding to the non-Gaussian tail of the distribution of $\ln T$. This tail differs drastically from that in the case of absorption. The physical meaning of typical and resonant realizations is discussed.

cond-mat↗

arXiv1996

Theory of random matrices with strong level confinement

Unitary ensembles of large N x N random matrices with a non-Gaussian probability distribution P[H] ~ exp{-TrV[H]} are studied using a theory of polynomials orthogonal with respect to exponential weights. Asymptotically exact expressions for density of levels, one- and two-point Green's functions are calculated. We show that in the large-N limit the properly rescaled local eigenvalue correlations are independent of P[H] while global smoothed connected correlations depend on P[H] only through the endpoints of spectrum. We also establish previously unknown intimate connection between structure of Szegö function entering strong polynomial asymptotics and mean-field equation by Dyson.

cond-mat↗

arXiv1996

Theory of random matrices with strong level confinement: orthogonal polynomial approach

Strongly non-Gaussian ensembles of large random matrices possessing unitary symmetry and logarithmic level repulsion are studied both in presence and absence of hard edge in their energy spectra. Employing a theory of polynomials orthogonal with respect to exponential weights we calculate with asymptotic accuracy the two-point kernel over all distance scale, and show that in the limit of large dimensions of random matrices the properly rescaled local eigenvalue correlations are independent of level confinement while global smoothed connected correlations depend on confinement potential only through the endpoints of spectrum. We also obtain exact expressions for density of levels, one- and two-point Green's functions, and prove that new universal local relationship exists for suitably normalized and rescaled connected two-point Green's function. Connection between structure of Szegö function entering strong polynomial asymptotics and mean-field equation is traced.

cond-mat↗