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Tensor network states constitute an important variational set of quantum states for numerical studies of strongly correlated systems in condensed-matter physics, as well as in mathematical physics. This is specifically true for finitely…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
Interfaces in materials are often treated as massless geometric boundaries, and many kinetic models adopt an overdamped assumption. In this Letter, we show that grain boundaries exhibit inertial behavior under high-frequency oscillatory…
When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s).…
We study the problem of computing energy density in one-dimensional quantum systems. We show that the ground-state energy per site or per bond can be computed in time (i) independent of the system size and subexponential in the desired…
We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A…
How do we search for the entire family tree without unwanted random guesses, starting from a high-index and high-energy stationary state on the energy landscape? Here we introduce a general numerical method that constructs the pathway map…
Many biological, chemical, and physical systems are underpinned by stochastic transitions between equilibrium states in a potential energy. Here, we consider such transitions in a minimal model with two possible competing pathways, both…
By using numerical simulations, we investigate the dynamics of a quantum system of interacting bosons. We find an increase of properly defined mixing properties when the number of particles increases at constant density or the interaction…
We discuss the universal dynamics of elastic interfaces in quenched random media. We focus in the relation between the rough geometry and collective transport properties in driven steady-states. Specially devised numerical algorithms allow…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such…
The electromagnetic interaction is characterised by discrete states for bound systems in contrast to continuous states for unbound systems. The difference merely arises because the characteristic equations do not exhibit the same behaviour…
Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
The dynamics of a many-particle system are often modeled by mapping the Hamiltonian onto a Schr\"odinger equation. An alternative approach is to solve the Hamiltonian equations directly in a model space of many-body configurations. In a…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems -- similar to how phase transitions only sharply emerge in the thermodynamic limit. The resulting…
We analyze the energy barriers that allow escapes from a given local minimum in a mean-field model of glasses. We perform this study by using the Kac-Rice method and computing the typical number of critical points of the energy function at…
In this paper, the problem of state and input constrained control is addressed, with multidimensional constraints. We obtain a local description of the boundary of the admissible subset of the state space where the state and input…