Condensed Matter

The random sequential adsorption (RSA) of identical elongated particles (discorectangles) on a line ("Paris car parking problem") was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The possible orientations of the discorectanles were restricted between θ∈[− θ m ; θ m ] while the aspect ratio (length-to-width ratio) for the discorectangles was varied within the range ε∈[1;100] . Additionally, the limiting case ε=∞ (i.e., widthless sticks) was considered. We observed, that the RSA deposition for the problem under consideration was governed by the formation of rarefied holes (containing particles oriented along a line) surrounded by comparatively dense stacks (filled with almost parallel particles oriented in the vertical direction). The kinetics of the changes of the order parameter, and the packing density are discussed. Partial ordering of the discorectangles significantly affected the packing density at the jamming state, φ j , and shifted the cusps in the φ j (ε) dependencies. This can be explained by the effects on the competition between the particles' orientational degrees of freedom and the excluded volume effects.

We construct a three-dimensional (3D), time-reversal symmetric generalization of the Chalker-Coddington network model for the integer quantum Hall transition. The novel feature of our network model is that in addition to a weak topological insulator phase already accommodated by the network model framework in the pre-existing literature, it hosts strong topological insulator phases as well. We unambiguously demonstrate that strong topological insulator phases emerge as intermediate phases between a trivial insulator phase and a weak topological phase. Additionally, we found a non-local transformation that relates a trivial insulator phase and a weak topological phase in our network model. Remarkably, strong topological phases are mapped to themselves under this transformation. We show that upon adding sufficiently strong disorder the strong topological insulator phases undergo phase transitions into a metallic phase. We numerically determine the critical exponent of the insulator-metal transition. Our network model explicitly shows how a semi-classical percolation picture of topological phase transitions in 2D can be generalized to 3D and opens up a new venue for studying 3D topological phase transitions.

Macroscopic spin ensembles possess brain-like features such as non-linearity, plasticity, stochasticity, selfoscillations, and memory effects, and therefore offer opportunities for neuromorphic computing by spintronics devices. Here we propose a physical realization of artificial neural networks based on magnetic textures, which can update their weights intrinsically via built-in physical feedback utilizing the plasticity and large number of degrees of freedom of the magnetic domain patterns and without resource-demanding external computations. We demonstrate the idea by simulating the operation of a 4-node Hopfield neural network for pattern recognition.

Networks that have power-law connectivity, commonly referred to as the scale-free networks, are an important class of complex networks. A heterogeneous mean-field approximation has been previously proposed for the Ising model of the Barabási-Albert model of scale-free networks with classical spins on the nodes wherein it was shown that the critical temperature for such a system scales logarithmically with network size. For finite sizes, there is no criticality for such a system and hence no true phase transition in terms of singular behavior. Further, in the thermodynamic limit, the mean-field prediction of an infinite critical temperature for the system may exclude any true phase transition even then. Nevertheless, with an eye on potential applications of the model on biological systems that are generally finite, one may still try to find approximations that describe the relevant observables quantitatively. Here we present an alternative, approximate formulation for the description of the Ising model of a Barabási-Albert Network. Using the classical definition of magnetization, we show that Ising models on a network can be well-approximated by a long-range interacting homogeneous Ising model wherein each node of the network couples to all other spins with a strength determined by the mean degree of the Barabási-Albert Network. In such an effective long-range Ising model of a Barabási-Albert Network, the critical temperature is directly proportional to the number of preferentially attached links added to grow the network. The proposed model describes the magnetization of the majority of the sites with average or smaller than average degree better compared to the heterogeneous mean-field approximation. The long-range Ising model is the only homogeneous description of Barabási-Albert networks that we know of.

Spin-glass systems are universal models for representing many-body phenomena in statistical physics and computer science. High quality solutions of NP-hard combinatorial optimization problems can be encoded into low energy states of spin-glass systems. In general, evaluating the relevant physical and computational properties of such models is difficult due to critical slowing down near a phase transition. Ideally, one could use recent advances in deep learning for characterizing the low-energy properties of these complex systems. Unfortunately, many of the most promising machine learning approaches are only valid for distributions over continuous variables and thus cannot be directly applied to discrete spin-glass models. To this end, we develop a continuous probability density theory for spin-glass systems with arbitrary dimensions, interactions, and local fields. We show how our formulation geometrically encodes key physical and computational properties of the spin-glass in an instance-wise fashion without the need for quenched disorder averaging. We show that our approach is beyond the mean-field theory and identify a transition from a convex to non-convex energy landscape as the temperature is lowered past a critical temperature. We apply our formalism to a number of spin-glass models including the Sherrington-Kirkpatrick (SK) model, spins on random Erdős-Rényi graphs, and random restricted Boltzmann machines.

The many-body localised (MBL) to thermal crossover observed in exact diagonalisation studies remains poorly understood as the accessible system sizes are too small to be in an asymptotic scaling regime. We develop a model of the crossover in short 1D chains in which the MBL phase is destabilised by the formation of many-body resonances. The model reproduces several properties of the numerically observed crossover, including an apparent correlation length exponent ν=1 , exponential growth of the Thouless time with disorder strength, linear drift of the critical disorder strength with system size, scale-free resonances, apparent 1/? dependence of disorder-averaged spectral functions, and sub-thermal entanglement entropy of small subsystems. In the crossover, resonances induced by a local perturbation are rare at numerically accessible system sizes L which are smaller than a \emph{resonance length} λ . For L??λ ??????, resonances typically overlap, and this model does not describe the asymptotic transition. The model further reproduces controversial numerical observations which Refs. [?untajs et al, 2019] and [Sels & Polkovnikov, 2020] claimed to be inconsistent with MBL. We thus argue that the numerics to date is consistent with a MBL phase in the thermodynamic limit.

Dyson insulators with random hoppings in a lattice approach localization faster compared to the usual Anderson insulators with site disorder. For even- N lattice sites the Dyson insulators mimic topological insulators with a pseudo-gap at the band center and the energy-level statistics obtained via the P(S) distribution is of an intermediate type close to the Anderson localized Poisson limit. For odd- N level-repulsion and Wigner statistics appears as in the quasi-metallic regime of 2D Anderson insulators, plus a single E=0 mode protected by chiral symmetry. The distribution of the participation ratio and the multifractal dimensions of the midband state are computed. In 1D the Dyson state is localized and in 2D is fractal. Our results might be relevant for recent experimental studies of chiral localization in photonic waveguide arrays.

A novel method for the calculation of eigenfrequencies of non-uniformly filled spherical cavity resonators is developed. The impact of the system symmetry on the electromagnetic field distribution as well as on its degrees of freedom (the set of resonant modes) is examined. It is shown that in the case of angularly symmetric cavity, regardless of its radial non-uniformity, the set of resonator modes is, as anticipated, a superposition of TE and TM oscillations which can be described in terms of a single scalar function independently of each other. The spectrum is basically determined through the introduction of effective ``dynamic'' potentials which encode the infill inhomogeneity. The violation of polar symmetry in the infill dielectric properties, the azimuthal symmetry being simultaneously preserved, suppresses all azimuthally non-uniform modes of electric-type (TM) oscillations. In the absence of angular symmetry of both electric and magnetic properties of the resonator infill, only azimuthally uniform distribution of both TM and TE fields is expected to occur in the resonator. The comparison is made of the results obtained through the proposed method and of the test problem solution obtained with use of commercial solvers. The method appears to be efficient for computational complex algorithms for solving spectral problems, including those for studying the chaotic properties of electrodynamic systems' spectra.

Generalized linear models are one of the most efficient paradigms for predicting the correlated stochastic activity of neuronal networks in response to external stimuli, with applications in many brain areas. However, when dealing with complex stimuli, the inferred coupling parameters often do not generalize across different stimulus statistics, leading to degraded performance and blowup instabilities. Here, we develop a two-step inference strategy that allows us to train robust generalized linear models of interacting neurons, by explicitly separating the effects of correlations in the stimulus from network interactions in each training step. Applying this approach to the responses of retinal ganglion cells to complex visual stimuli, we show that, compared to classical methods, the models trained in this way exhibit improved performance, are more stable, yield robust interaction networks, and generalize well across complex visual statistics. The method can be extended to deep convolutional neural networks, leading to models with high predictive accuracy for both the neuron firing rates and their correlations.

Glasses and disordered materials are known to display anomalous features in the density of states, in the specific heat and in thermal transport. Nevertheless, in recent years, the question whether these properties are really anomalous (and peculiar of disordered systems) or rather more universal than previously thought, has emerged. New experimental and theoretical observations have questioned the origin of the boson peak and the linear in T specific heat exclusively from disorder and TLS. The same properties have been indeed observed in ordered or minimally disordered compounds and in incommensurate structures for which the standard explanations are not applicable. Using the formal analogy between phason modes (e.g. in quasicrystals and incommensurate lattices) and diffusons, and between amplitude modes and optical phonons, we suggest the existence of a more universal physics behind these properties. In particular, we strengthen the idea that linear in T specific heat is linked to low energy diffusive modes and that a BP excess can be simply induced by gapped optical-like modes.