Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. While these states and their phase transitions have been studied extensively with mean field theory, the validity of the mean field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.

We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. The method allows us to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments.

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold gases of Rydberg atoms, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, non-equilibrium setting of cavity-QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability---a foundational and patently non-equilibrium model of cavity-QED---the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by identifying a limit in which the quantum dynamics is asymptotically equivalent to non-equilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, producing results consistent with the behavior of a finite-temperature Ising model.Comment: 11 pages + appendices, 8 figure

Continuous symmetry breaking (CSB) in low-dimensional systems, forbidden by the Mermin-Wagner theorem for short-range interactions, may take place in the presence of slowly decaying long-range interactions. Nevertheless, there is no stringent bound on how slowly interactions should decay to give rise to CSB in 1D quantum systems at zero temperature. Here, we study a long-range interacting spin chain with U(1) symmetry and power-law interactions V(r)∼1/r^{α}. Using a number of analytical and numerical techniques, we find CSB for α smaller than a critical exponent α_{c}(≤3) that depends on the microscopic parameters of the model. Furthermore, the transition from the gapless XY phase to the gapless CSB phase is mediated by the breaking of conformal and Lorentz symmetries due to long-range interactions, and is described by a universality class akin to, but distinct from, the Berezinskii-Kosterlitz-Thouless transition. Signatures of the CSB phase should be accessible in existing trapped-ion experiments.

Long-range quantum lattice systems often exhibit drastically different behavior than their shortrange counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model with long-range interactions, and a fermionic model with long-range hopping and pairing terms, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of the long-range couplings, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent.

We study the quantum electrodynamics vacuum in the presence of a body rotating along its axis of symmetry and show that the object spontaneously emits energy if it is lossy. The radiated power is expressed as a general trace formula solely in terms of the scattering matrix, making an explicit connection to the conjecture of Zel'dovich [JETP Lett. 14, 180 (1971)] on rotating objects. We further show that a rotating body drags along nearby objects while making them spin parallel to its own rotation axis.

We present a number of arguments to demonstrate that a quantum analog of the Cherenkov effect occurs when two non-dispersive half-spaces are in relative motion. We show that they experience friction beyond a threshold velocity which, in their center-of-mass frame, is the phase speed of light within their medium, and the loss in mechanical energy is radiated through the medium before getting fully absorbed in the form of heat. By deriving various correlation functions inside and outside the two half-spaces we explicitly compute this radiation, and discuss its dependence on the reference frame.

We consider polymers attached to the tip of a cone, and the resulting force due to entropy loss on approaching a plate (or another cone). At separations shorter than the polymer radius of gyration Rg, the only relevant length scale is the tip-plate (or tip-tip) separation h, and the entropic force is given by F = A kBT /h. The universal amplitude A can be related to (geometry dependent) correlation exponents of long polymers. We compute A for phantom polymers, and for self-avoiding (including star) polymers by ǫ-expansion, as well as by numerical simulations in 3 dimensions.PACS numbers: 64.60. Single molecule manipulation [1-5] using techniques such as atomic force microscopy (AFM) [6], microneedles [7], optical [8,9] and magnetic [10] tweezers enable extremely detailed study of geometry and forces in long polymers. The positional accuracy of AFM tip [5,11] can be as good as few nm, while the forces of order of 1 pN can be measured, and measurements can be carried out in almost biological conditions [12,13]. These enhanced sensitivities bring us to the range where entropic forces of long polymers in a solvent can be significant even when the deformation of the polymer is relatively slight. While the main thrust of the experimental research is extraction of specific information from the force-displacement behaviors of the polymers, certain features are independent of the microscopic details [14], but depend on the probe shape, as discussed in this work.We consider an idealized set-up in which a polymer is attached to the tip of a solid cone. The cone approaching a plate (or another cone) exemplifies a geometry in which the only (non-microscopic) length scale is provided by the tip-plate (or tip-tip) separation h. Fluctuating polymers typify self-similar variations at scales intermediate between microscopic (persistence length a) and macroscopic. The latter is set by the radius of gyration which grows with the number of monomers through the scaling relation R g ∝ N ν . Thus when a cone-tip-attached polymer approaches a plate, at separations a ≪ h ≪ R g the only relevant length scale is h, and on dimensional grounds, the force due to loss of entropy must behave asSuch a force law should apply to all circumstances where the separation provides the only relevant length scale.The amplitude A will depend on geometric factors such as the opening angle of the cone Θ (and if tilted, on the corresponding angle). One could presume, that the dimensionless amplitude may also depend on microscopic * Email: magrebi@mit.edu properties on the polymer. However, in case of cone-tippolymers we shall demonstrate that the amplitude A can be related to universal (and shape dependent) polymer exponents. The simple force law of Eq.(1) follows easily from various polymer scaling forms (see, e.g. the derivation below) such as in Refs. [15][16][17], and should be part of polymer lore. Surprisingly, we could not find an explicit reference to it in any of the standard polymer textbooks. A polymer attached to the tip of an AFM is approximate...