Explore the vast range of titles available.

This book opens with a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics, and moves on to cover lattice field theory, spin systems, gauge theories and more. Each chapter ends with illustrative problems.

For a one-dimensional spin chain with random local interactions, we prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system. The construction uses a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors.

The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we (i) pay debts to heroic predecessors, (ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, (iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, (iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of d=∞ KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.

A molecular network can be characterized by several different ways, like a matrix, a polynomial, a drawing or a topological descriptor. A topological descriptor is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. Analyzing and determining the topological indices and structural properties of a network or a graph have been a worthy studied topic in the field of chemistry, networks analysis, etc. In this paper, we consider several types of the generalized Sierpiński networks and investigate the explicit expressions of some well-known valency-based topological indices. Taking into account the other structural property of the generalized Sierpiński networks, the average degree is determined.

Communication constraint is the main factor that affects networked autonomous underwater vehicles’ (NAUVs) control performance. This article investigates the distributed event-driven formation control for NAUVs undergoing external disturbances and uncertain hydrodynamics. As distributed systems, the achievement of the target geometrical configuration hinges heavily on neighboring communication. However, the risk of traffic jamming will arise when an underwater acoustic communication network is occupied by multiple information packets broadcasted from different vehicles. Worse still, potential packet losses and time delays caused by traffic jamming may destroy the system stability. Regarding this, by introducing a distributed observer for each vehicle, the leader-follower distributed formation control is categorized into a localization layer and a tracking layer. Furthermore, a trade-off between communication constraint and control performance is achieved under this framework. Specifically, a novel interleaved periodic dynamic event-triggered communication mechanism is integrated into the upper distributed observer, endowing NAUVs with anti-competing interaction capability. By resorting to an anti-winding finite-time prescribed performance algorithm in the lower tracking layer, the tracking accuracy is guaranteed even in circumstances of large-angle formation motions. The prominent feature of the proposed control scheme lies in ensuring the formation flexibility and tracking accuracy under unreliable communication network. Simulation results are constructed to illustrate the effectiveness of this work.

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z2 -even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Δσ=0.518154(15) , and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.

We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face.

We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are often not effective and sufficient to contain them. Many common approaches do not provide a good picture of the actual system behavior, because they neglect feedback loops, instabilities and cascade effects. The complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be better understood by means of complexity science. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.

We consider quantum stochastic processes and discuss a level 2.5 large deviation formalism providing an explicit and complete characterisation of fluctuations of time-averaged quantities, in the large-time limit. We analyse two classes of quantum stochastic dynamics, within this framework. The first class consists of the quantum jump trajectories related to photon detection; the second is quantum state diffusion related to homodyne detection. For both processes, we present the level 2.5 functional starting from the corresponding quantum stochastic Schrödinger equation and we discuss connections of these functionals to optimal control theory.

In Krotov et al. (in: Lee (eds) Advances in Neural Information Processing Systems, Curran Associates, Inc., Red Hook, 2016) Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the model. We prove this claim and take the ”limit” as the degree of the polynomial becomes infinite, i.e. an exponential interaction function. With this interaction we prove that model has an exponential storage capacity in the number of neurons, yet the basins of attraction are almost as large as in the standard Hopfield model.