Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComment on Effective confining potential of quantum states in disordered media
132
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We provide some analytical tests of the density of states estimation from the localization landscape approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.
rate research
Read More
By using very general arguments, we show that the entropy loss conjecture at the glass transition violates the second law of thermodynamics and must be rejected.
We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.
We explore numerically, analytically, and experimentally the relationship between quasi-normal modes (QNMs) and transmission resonance (TR) peaks in the transmission spectrum of one-dimensional (1D) and quasi-1D open disordered systems. It is shown that for weak disorder there exist two types of the eigenstates: ordinary QNMs which are associated with a TR, and hidden QNMs which do not exhibit peaks in transmission or within the sample. The distinctive feature of the hidden modes is that unlike ordinary ones, their lifetimes remain constant in a wide range of the strength of disorder. In this range, the averaged ratio of the number of transmission peaks $N_{rm res}$ to the number of QNMs $N_{rm mod}$, $N_{rm res}/N_{rm mod}$, is insensitive to the type and degree of disorder and is close to the value $sqrt{2/5}$, which we derive analytically in the weak-scattering approximation. The physical nature of the hidden modes is illustrated in simple examples with a few scatterers. The analogy between ordinary and hidden QNMs and the segregation of superradiant states and trapped modes is discussed. When the coupling to the environment is tuned by an external edge reflectors, the superradiace transition is reproduced. Hidden modes have been also found in microwave measurements in quasi-1D open disordered samples. The microwave measurements and modal analysis of transmission in the crossover to localization in quasi-1D systems give a ratio of $N_{rm res}/N_{rm mod}$ close to $sqrt{2/5}$. In diffusive quasi-1D samples, however, $N_{rm res}/N_{rm mod}$ falls as the effective number of transmission eigenchannels $M$ increases. Once $N_{rm mod}$ is divided by $M$, however, the ratio $N_{rm res}/N_{rm mod}$ is close to the ratio found in 1D.
Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven systems, but there are many instances in which such instabilities are undesirable. Using parametric resonance as a model process, here we show that a range of states that would be destabilized by symmetry-breaking instabilities can be preserved and stabilized by the introduction of suitable system asymmetry. Because symmetric states are spatially homogeneous and asymmetric systems are spatially heterogeneous, we refer to this effect as heterogeneity-stabilized homogeneity. We illustrate this effect theoretically using driven pendulum array models and demonstrate it experimentally using Faraday wave instabilities. Our results have potential implications for the mitigation of instabilities in engineered systems and the emergence of homogeneous states in natural systems with inherent heterogeneities.
We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent $gamma$ (called the $gamma$-ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with $gamma=1$ (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the $gamma$-ensembles. It enables us to numerically compute the eigenvalue density of $gamma$-ensembles for all $gamma > 0$. We show that one important effect of the two-particle interaction parameter $gamma$ is to generate or enhance the non-monotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing $gamma$ can lead to a large non-monotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of $gamma$-ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
