Related papers: Correlation functions of integrable models: a desc…
We show that a class of random all-to-all spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram due to the pairwise separable nature of the couplings. By controlling the…
Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced BCS model Hamiltonian. We show that this model is integrable by the algebraic Bethe…
A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few…
In this paper we investigate an integrable loop model and its connection with a supersymmetric spin chain. The Bethe Ansatz solution allows us to study some properties of the ground state. When the loop fugacity $q$ lies in the physical…
The increasing complexity of AI systems has made understanding their behavior critical. Numerous interpretability methods have been developed to attribute model behavior to three key aspects: input features, training data, and internal…
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal…
The physics of the attractive one-dimensional Bose gas (Lieb-Liniger model) is investigated with techniques based on the integrability of the system. Combining a knowledge of particle quasi-momenta to exponential precision in the system…
The correlation functions for a strongly correlated exactly solvable one-dimensional boson system on a finite chain as well as in the thermodynamic limit are calculated explicitly. This system which we call the phase model is the strong…
This work investigates the intricate relationship between the q-boson model, a quantum integrable system, and classical integrable systems such as the Toda and KP hierarchies. Initially, we analyze scalar products of off-shell Bethe states…
The recent advances in angle resolved photoemission techniques allowed the unambiguous experimental confirmation of spin charge decoupling in quasi one dimensional (1D) Mott insulators. This opportunity stimulates a quantitative analysis of…
The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
Discovery of causal relations is fundamental for understanding the dynamics of complex systems. While causal interactions are well defined for acyclic systems that can be separated into causally effective subsystems, a mathematical…
Capsule networks (see e.g. Hinton et al., 2018) aim to encode knowledge of and reason about the relationship between an object and its parts. In this paper we specify a generative model for such data, and derive a variational algorithm for…
We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…
We review the basic notion of correlations in point processes, adapted to the language of high energy physicists. The measurement of accessible information on correlations by means of correlation integrals is summarized. Applications to the…
Generalized Hydrodynamics is a recent theory that describes large scale transport properties of one dimensional integrable models. It is built on the (typically infinitely many) local conservation laws present in these systems, and leads to…
An improved unified formulation based on the effective field theory is introduced for a spin-1 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
We extend a recent construction for an integrable model describing Josephson tunneling between identical BCS systems to the case where the BCS systems have different single particle energy levels. The exact solution of the generalized model…
Articulated objects like doors, drawers, valves, and tools are pervasive in our everyday unstructured dynamic environments. Articulation models describe the joint nature between the different parts of an articulated object. As most of these…