arXiv subjects

Austen Lamacraft

Publications and source records attributed to Austen Lamacraft.

At least 37 records · Page 2Linked to original sources

arXiv2019

Learning Symmetries of Classical Integrable Systems

The solution of problems in physics is often facilitated by a change of variables. In this work we present neural transformations to learn symmetries of Hamiltonian mechanical systems. Maintaining the Hamiltonian structure requires novel network architectures that parametrize symplectic transformations. We demonstrate the utility of these architectures by learning the structure of integrable models. Our work exemplifies the adaptation of neural transformations to a family constrained by more than the condition of invertibility, which we expect to be a common feature of applications of these methods.

physics.comp-ph↗

arXiv2019

Unitary circuits of finite depth and infinite width from quantum channels

We introduce an approach to compute reduced density matrices for local quantum unitary circuits of finite depth and infinite width. Suppose the time-evolved state under the circuit is a matrix-product state with bond dimension $D$; then the reduced density matrix of a half-infinite system has the same spectrum as an appropriate $D\times D$ matrix acting on an ancilla space. We show that reduced density matrices at different spatial cuts are related by quantum channels acting on the ancilla space. This quantum channel approach allows for efficient numerical evaluation of the entanglement spectrum and Rényi entropies and their spatial fluctuations at finite times in an infinite system. We benchmark our numerical method on random unitary circuits, where many analytic results are available, and also show how our approach analytically recovers the behaviour of the kicked Ising model at the self-dual point. We study various properties of the spectra of the reduced density matrices and their spatial fluctuations in both the random and translation-invariant cases.

quant-ph↗

arXiv2019

Quantum Brownian motion in a quasiperiodic potential

We consider a quantum particle subject to Ohmic dissipation, moving in a bichromatic quasiperiodic potential. In a periodic potential the particle undergoes a zero-temperature localization-delocalization transition as dissipation strength is decreased. We show that the delocalized phase is absent in the quasiperiodic case, even when the deviation from periodicity is infinitesimal. Using the renormalization group, we determine how the effective localization length depends on the dissipation. We show that {a similar problem can emerge in} the strong-coupling limit of a mobile impurity moving in a periodic lattice and immersed in a one-dimensional quantum gas.

cond-mat.quant-gas↗

arXiv2018

Phases of quantum dimers from ensembles of classical stochastic trajectories

We study the connection between the phase behaviour of quantum dimers and the dynamics of classical stochastic dimers. At the so-called Rokhsar-Kivelson (RK) point a quantum dimer Hamiltonian is equivalent to the Markov generator of the dynamics of classical dimers. A less well understood fact is that away from the RK point the quantum-classical connection persists: in this case the Hamiltonian corresponds to a non-stochastic "tilted" operator that encodes the statistics of time-integrated observables of the classical stochastic problem. This implies a direct relation between the phase behaviour of quantum dimers and properties of ensembles of stochastic trajectories of classical dimers. We make these ideas concrete by studying fully packed dimers on the square lattice. Using transition path sampling - supplemented by trajectory umbrella sampling - we obtain the large deviation statistics of dynamical activity in the classical problem, and show the correspondence between the phase behaviour of the classical and quantum systems. The transition at the RK point between quantum phases of distinct order corresponds, in the classical case, to a trajectory phase transition between active and inactive dynamical phases. Furthermore, from the structure of stochastic trajectories in the active dynamical phase we infer that the ground state of quantum dimers has columnar order to one side of the RK point. We discuss how these results relate to those from quantum Monte Carlo, and how our approach may generalise to other problems.

cond-mat.stat-mech↗

arXiv2018

Infinite Lattices of Vortex Molecules in Rabi-Coupled Condensates

Vortex molecules can form in a two component superfluid when a Rabi field drives transitions between the two components. We study the ground state of an infinite system of vortex molecules in 2D, using a numerical scheme which makes no use of the lowest Landau level approximation. We find the ground state lattice geometry for different values of inter-component interactions and strength of the Rabi field. In the limit of large field when molecules are tightly bound, we develop a complimentary analytical description. The energy governing the alignment of molecules on a triangular lattice is found to correspond to that of an infinite system of 2D quadrupoles, which may be written in terms of an elliptic function $\mathcal{Q}(z_{ij};ω_1 , ω_2 )$. This allows for a numerical evaluation of the energy which enables us to find the ground state configuration of the molecules.

cond-mat.quant-gas↗

arXiv2018

Noisy Spins and the Richardson-Gaudin Model

We study a system of spins (qubits) coupled to a common noisy environment, each precessing at its own frequency. The correlated noise experienced by the spins implies long-lived correlations that relax only due to the differing frequencies. We use a mapping to a non-Hermitian integrable Richardson-Gaudin model to find the exact spectrum of the quantum master equation in the high-temperature limit, and hence determine the decay rate. Our solution can be used to evaluate the effect of inhomogeneous splittings on a system of qubits coupled to a common bath.

quant-ph↗

arXiv2017

Nonlinear Luttinger liquid: Exact result for the Green function in terms of the fourth Painlevé transcendent

We show that exact time dependent single particle Green function in the Imambekov-Glazman theory of nonlinear Luttinger liquids can be written, for any value of the Luttinger parameter, in terms of a particular solution of the Painlevé IV equation. Our expression for the Green function has a form analogous to the celebrated Tracy-Widom result connecting the Airy kernel with Painlevé II. The asymptotic power law of the exact solution as a function of a single scaling variable $x/\sqrt{t}$ agrees with the mobile impurity results. The full shape of the Green function in the thermodynamic limit is recovered with arbitrary precision via a simple numerical integration of a nonlinear ODE.

cond-mat.quant-gas↗

arXiv2015

Quantum Hydrodynamics in One Dimension beyond the Luttinger Liquid

Recent years have seen the development of a rich phenomenology beyond the Luttinger Liquid model of one dimensional quantum fluids, arising from interactions between the elementary phonon excitations. It has been known for some time, however, that the straightforward inclusion of these interactions presents technical difficulties that have necessitated approaches based on refermionization or effective impurity models. In this work we show that the nonlinear extensions of the Luttinger model are tractable in the phonon basis. We present a calculation of the singularities present in the zero temperature dynamical structure factor in the semiclassical limit where the phonon dispersion is strong. A unitary transformation decouples interactions between left-- and right--moving phonons, leaving a nonlinear chiral Hamiltonian. At low momenta, this Hamiltonian has a spectrum bounded above and below by thresholds identified with phonon and soliton excitations in the semiclassical limit. The chiral dynamical structure factor therefore has support only in this region, with power law singularities at the thresholds originating in the Anderson orthogonality catastrophe, which we calculate analytically. The dynamical structure factor for the original nonchiral Hamiltonian is a convolution of this chiral correlator with a power law arising from the left--right decoupling.

cond-mat.quant-gas↗

arXiv2014

The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics

We show that the resonant interactions between phonons in one dimension may be treated consistently within Quantum Hydrodynamics by the introduction of phonon dispersion. In this way the physics of a nonlinear Luttinger liquid may be described in terms of hydrodynamic (i.e. bosonized) variables without recourse to refermionization or the introduction of fictitious impurities. We focus on the calculation of the dynamic structure factor for a model with quadratic dispersion, which has the Benjamin--Ono equation of fluid dynamics as its equation of motion. We find singular behavior in the vicinity of upper and lower energetic thresholds corresponding to phonon and soliton branches of the classical theory, which may be benchmarked against known results for the Calogero--Sutherland model.

cond-mat.quant-gas↗

arXiv2012

Diffractive scattering of three particles in one dimension: a simple result for weak violations of the Yang--Baxter equation

We study scattering of three equal mass particles in one dimension. Integrable interactions are synonymous with non-diffractive scattering, meaning that the set of incoming momenta for any scattering event coincides with the set of outgoing momenta. A system is integrable if the two particle scattering matrix obeys the Yang--Baxter equation. Nonintegrable interactions correspond to diffractive scattering, where the set of outgoing momenta may take on all values consistent with energy and momentum conservation. Such processes play a vital role in the kinetics of one dimensional gases, where binary collisions are unable to alter the distribution function. When integrability is broken weakly, the result is a small diffractive scattering amplitude. Our main result is a simple formula for the diffractive part of the scattering amplitude, when the violation of the Yang--Baxter equation is small. Although the derivation is given for delta-function interactions, the result depends only on the two-particle scattering matrix, and should therefore also apply to finite-range interactions close to integrable.

cond-mat.quant-gas↗

arXiv2012

Critical velocity of a mobile impurity in one-dimensional quantum liquids

We study the notion of superfluid critical velocity in one spatial dimension. It is shown that for heavy impurities with mass $M$ exceeding a critical mass $M_\mathrm{c}$, the dispersion develops periodic metastable branches resulting in dramatic changes of dynamics in the presence of an external driving force. In contrast to smooth Bloch Oscillations for $M<M_\mathrm{c}$, a heavy impurity climbs metastable branches until it reaches a branch termination point or undergoes a random tunneling event, both leading to an abrupt change in velocity and an energy loss. This is predicted to lead to a non-analytic dependence of the impurity drift velocity on small forces.

cond-mat.quant-gas↗

arXiv2012

From GPE to KPZ: finite temperature dynamical structure factor of the 1D Bose gas

We study the finite temperature dynamical structure factor $S(k,ω)$ of a 1D Bose gas using numerical simulations of the Gross--Pitaevskii equation appropriate to a weakly interacting system. The lineshape of the phonon peaks in $S(k,ω)$ has a width $\propto |k|^{3/2}$ at low wavevectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar--Parisi--Zhang universality class of dynamical critical phenomena.

cond-mat.quant-gas↗

arXiv2011

Universal phase structure of dilute Bose gases with Rashba spin-orbit coupling

A Bose gas subject to a light-induced Rashba spin-orbit coupling possesses a dispersion minimum on a circle in momentum space; we show that kinematic constraints due to this dispersion cause interactions to renormalize to universal, angle-dependent values that govern the phase structure in the dilute-gas limit. We find that, regardless of microscopic interactions, (a) the ground state involves condensation at two opposite momenta, and is, in finite systems, a fragmented condensate; and (b) there is a nonzero-temperature instability toward the condensation of pairs of bosons. We discuss how our results can be reconciled with the qualitatively different mean-field phase diagram, which is appropriate for dense gases.

cond-mat.quant-gas↗

arXiv2011

Boson pairing and unusual criticality in a generalized XY model

We discuss the unusual critical behavior of a generalized XY model containing both 2π-periodic and π-periodic couplings between sites. The presence of vortices and half-vortices allows for single-particle condensate and pair-condensate phases. Using a field theoretic formulation and worm algorithm Monte Carlo simulations, we show that in two dimensions it is possible for the system to pass directly from the disordered (high temperature) phase to the single particle (quasi)-condensate via an Ising transition, a situation reminiscent of the `deconfined criticality' scenario.

cond-mat.stat-mech↗

arXiv2011

Potential insights into non-equilibrium behavior from atomic physics

This chapter seeks to outline a few basic problems in quantum statistical physics where recent experimental advances from the atomic physics community offer the hope of dramatic progress. The focus is on nonequilibrium situations where the powerful concepts and methods of equilibrium statistical physics and "linear response" theory (for small deviations from equilibrium) are not applicable. The problems discussed here are chosen in part because they have a high degree of "universality" or generality across different microscopic situations, as the major challenge in nonequilibrium statistical physics, both quantum and classical, has been to find principles as general as the basic principles of equilibrium statistical physics or linear response.

cond-mat.quant-gas↗

arXiv2011

Noise correlations in the expansion of an interacting 1D Bose gas from a regular array

We consider the one dimensional expansion of a system of interacting bosons, starting from a regular array. Without interactions the familiar Hanbury Brown and Twiss effect for bosons gives rise to a series of peaks in the density-density correlations of the expanded system. Infinitely repulsive particles likewise give a series of dips, a signature of the underlying description in terms of free fermions. In the intermediate case of finite interaction the noise correlations consist of a set of Fano resonance lineshapes, with an asymmetry parameter determined by the scattering phase shift of a pair of particles, and a width depending on the initial momentum spread of the particles.

cond-mat.quant-gas↗

arXiv2011

Spin 1 microcondensate in a magnetic field: semiclassics and exact solution

We study a spin 1 Bose condensate small enough to be treated as a single magnetic `domain': a system that we term a microcondensate. Because all particles occupy a single spatial mode, this quantum many body system has a well defined classical limit consisting of three degrees of freedom, corresponding to the three macroscopically occupied spin states. We study both the classical limit and its quantization, finding an integrable system in both cases. Depending on the sign of the ratio of the spin interaction energy and the quadratic Zeeman energy, the classical limit displays either a separartrix in phase space, or Hamiltonian monodromy corresponding to non-trivial phase space topology. We discuss the quantum signatures of these classical phenomena using semiclassical quantization as well as an exact solution using the Bethe ansatz.

cond-mat.quant-gas↗

arXiv2009

Low energy dynamics of spinor condensates

We present a derivation of the low energy Lagrangian governing the dynamics of the spin degrees of freedom in a spinor Bose condensate, for any phase in which the average magnetization vanishes. This includes all phases found within mean-field treatments except for the ferromagnet, for which the low energy dynamics has been discussed previously. The Lagrangian takes the form of a sigma model for the rotation matrix describing the local orientation of the spin state of the gas.

cond-mat.quant-gas↗