Latest Papers in Condensed Matter Physics

Statistical Mechanics

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Entanglement in a fermion chain under continuous monitoring (1804.04638v4)

Xiangyu Cao, Antoine Tilloy, Andrea De Luca

2018-04-12

We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.

Consensus ranking for multi-objective interventions in multiplex networks (1903.02059v2)

Márton Pósfai, Niklas Braun, Brianne A. Beisner, Brenda McCowan, Raissa M. D'Souza

2019-03-05

High-centrality nodes have disproportionate influence on the behavior of a network; therefore controlling such nodes can efficiently steer the system to a desired state. Existing multiplex centrality measures typically rank nodes assuming the layers are qualitatively similar. Many real systems, however, are comprised of networks heterogeneous in nature, for example, social networks may have both agnostic and affiliative layers. Here, we use rank aggregation methods to identify intervention targets in multiplex networks when the structure, the dynamics, and our intervention goals are qualitatively different for each layer. Our approach is to rank the nodes separately in each layer considering their different function and desired outcome, and then we use Borda count or Kemeny aggregation to identify a consensus ranking - top nodes in the consensus ranking are expected to effectively balance the competing goals simultaneously among all layers. To demonstrate the effectiveness of consensus ranking, we apply our method to a degree-based node removal procedure such that we aim to destroy the largest component in some layers, while maintaining large-scale connectivity in others. For any multi-objective intervention, optimal targets only exist in the Pareto-sense; we, therefore, use a weighted generalization of consensus ranking to investigate the trade-off between the competing objectives. We use a collection of model and real networks to systematically investigate how this trade-off is affected by multiplex network structure. We use the copula representation of the multiplex centrality distributions to generate model multiplex networks with given rank correlations. This allows use to separately manipulate the marginal centrality distribution of each layer and the interdependence between the layers and to independently investigate the role of the two using both analytical and numerical methods.

Hohenberg-Kohn theorems for interactions, spin and temperature (1906.03191v1)

Louis Garrigue

2019-06-07

We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain the information of the interactions and of the external potentials. Then, in the presence of the Zeeman interaction, a strong constraint on external fields is derived for systems having the same ground state densities and magnetizations. Next, we prove that the density and the entropy of a ground state contain the information of both the imposed external potential and temperature. Eventually, we conclude that at positive temperature, Hohenberg-Kohn theorems generically hold.

Particles, string and interface in the three-dimensional Ising model (1906.03176v1)

Gesualdo Delfino, Walter Selke, Alessio Squarcini

2019-06-07

We consider the three-dimensional Ising model sligthly below its critical temperature, with boundary conditions leading to the presence of an interface. We show how the interface and its fluctuations originate from the fundamental degrees of freedom of the continuum description, namely the particle modes of the underlying field theory. The product of the surface tension and the correlation length yields the particle density along the string whose propagation spans the interface. We also exactly determine the order parameter and energy density profiles across the interface, and show that they are in complete agreement with Monte Carlo simulations we perform. The variance of the interface fluctuations expressed in terms of the correlation length is half of that in two dimensions.

A thermodynamic description of turbulence as a source of stochastic kinetic energy for 3D self-assembly (1906.03166v1)

Per A. Löthman, Tijmen A. G. Hageman, Miko C. Elwenspoek, Gijs J. M. Krijnen, Massimo Mastrangeli, Andreas Manz, Leon Abelmann

2019-06-07

We investigate to what extent one can use a thermodynamic description of turbulent flow as a source of stochastic kinetic energy for three-dimensional self-assembly of magnetically interacting macroscopic particles. We confirm that the speed of the objects in the flow field generated in our system obeys the Maxwell--Boltzmann distribution, and their random walk can be defined by a diffusion coefficient following from the Einstein relation. However, we discovered that the analogy with Brownian dynamics breaks down when considering the directional components of the velocity. For the vectorial components, neither the equipartition theorem, nor the Einstein relation is obeyed. Moreover, the kinetic energy estimated from the random walk of individual objects is one order of magnitude higher than the value estimated from Boltzmann statistics on the interaction between two spheres with embedded magnets. These results show that introducing stochastic kinetic energy into a self-assembly process by means of turbulent flow can to a great extent be described by standard thermodynamic theory, but anisotropies and the specific nature of the interactions need to be taken into account.

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