arXiv subjects

Colin Rylands

Publications and source records attributed to Colin Rylands.

42 records · Page 3Linked to original sources

arXiv2019

Quantum Work of an Optical Lattice

A classic example of a quantum quench concerns the release of a interacting Bose gas from an optical lattice. The local properties of quenches such as this have been extensively studied however the global properties of these non-equilibrium quantum systems have received far less attention. Here we study several aspects of global non-equilibrium behavior by calculating the amount of work done by the quench as measured through the work distribution function. Using Bethe Ansatz techniques we determine the Loschmidt amplitude and work distribution function of the Lieb-Liniger gas after it is released from an optical lattice. We find the average work and its universal edge exponents from which we determine the long time decay of the Loshcmidt echo and highlight striking differences caused by the the interactions as well as changes in the geometry of the system. We extend our calculation to the attractive regime of the model and show that the system exhibits properties similar to the super Tonks-Girardaeu gas. Finally we examine the prominent role played by bound states in the work distribution and show that, with low probability, they allow for work to be extracted from the quench.

cond-mat.str-el↗

arXiv2019

Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model

A Luttinger Liquid coupled to a quantum impurity describes a large number of physical systems. The Hamiltonian consists of left- and right-moving fermions interacting among themselves via a density-density coupling and scattering off a localised transmitting and reflecting impurity. We solve exactly the Hamiltonian by means of an incoming-outgoing scattering Bethe basis which properly incorporates all scattering processes. A related model, the Weak-Tunnelling model, wherein the impurity is replaced by a tunnel junction, is solved by the same method. The consistency of the construction is established through a generalised Yang-Baxter relation. Periodic boundary conditions are imposed and the resulting Bethe Ansatz equations are derived by means of the Off Diagonal Bethe Ansatz approach. We derive the spectrum of the model for all coupling constant regimes and calculate the impurity free energy. We discuss the low energy behaviour of the systems for both repulsive and attractive interactions.

cond-mat.str-el↗

arXiv2019

Loschmidt Amplitude and Work Distribution in Quenches of the Sine-Gordon Model

The Sine-Gordon - equivalently, the massive Thirring - Hamiltonian is ubiquitous in low-dimensional physics, with applications that range from cold atom and strongly correlated systems to quantum impurities. We study here its non-equilibrium dynamics using the quantum quench protocol - following the system as it evolves under the Sine-Gordon Hamiltonian from initial Mott type states with large potential barriers. By means of the Bethe Ansatz we calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing these quenches for different values of the interaction strength. Some universal features are noted as well as an interesting duality relating quenches in different parameter regimes of the model.

cond-mat.str-el↗

arXiv2018

Simplified Thermodynamics for Quantum Impurity Models

Quantum impurity models play an important role in many areas of physics from condensed matter to AMO and quantum information. They are important models for many physical systems but also provide key insights to understanding much more complicated scenarios. In this paper we introduce a simplified method to describe the thermodynamic properties of integrable quantum impurity models. We show this method explicitly using the anisotropic Kondo and the interacting resonant level models. We derive a simplified expression for the free energy of both models in terms of a single physically transparent integral equation which is valid at all temperatures and values of the coupling constants.

cond-mat.str-el↗

arXiv2018

Quantum Dot in Interacting Environments

A quantum impurity attached to an interacting quantum wire gives rise to an array of of new phenomena. Using Bethe Ansatz we solve exactly models describing two geometries of a quantum dot coupled to an interacting quantum wire: a quantum dot that is (i) side-coupled and (ii) embedded in a Luttinger liquid. We find the eigenstates and determine the spectrum through the Bethe Ansatz equations. Using this we derive exact expressions for the ground state dot occupation. The thermodynamics are then studied using the thermodynamics Bethe Ansatz equations. It is shown that at low energies the dot becomes fully hybridized and acts as a backscattering impurity or tunnel junction depending on the geometry and furthermore that the two geometries are related by changing the sign of the interactions. Although remaining strongly coupled for all values of the interaction in the wire, there exists competition between the tunneling and backscattering leading to a suppression or enhancement of the dot occupation depending on the sign of the bulk interactions.

cond-mat.str-el↗

arXiv2014

Time Evolution of Superradiance

The superradiant behaviour of the Dicke model is examined using the Yudson representation. This is achieved by computing the time evolution of the mean photon current density and photon number. Extensions of this model including energy splitting and spatial separation are then investigated using this technique.

physics.optics↗