Abstract Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the spectrum whilst the scattering matrix is diagonal and solves the usual bootstrap equations. In the standard scattering picture, unstable particles result from complex poles of the S-matrix located in the unphysical sheet of rapidity space. Since they are not part of the asymptotic spectrum, their presence is only felt through the effect they have on physical quantities associated either to the theory as a whole (i.e. scaling functions, correlation functions) or to the stable particles themselves (i.e. energy/particle density). In two recent publications, the effect of unstable particles in different out-of-equilibrium settings has been studied. It has been shown that their presence is associated with specific signatures in many quantities of physical interest. A good way to select those quantities is to adopt the generalised hydrodynamic approach and to consider the effective velocities and particle densities of the stable particles in the theory. For an initial state given by a spacial gaussian profile of temperatures peaked at the origin, time evolution gives rise to particle and spectral particle densities that exhibit hallmarks of the creation and decay of unstable particles. While these signatures have been observed numerically elsewhere, this paper explores their quantitative and qualitative dependence on the parameters of the problem. We also consider other initial states characterised by “inverted gaussian” and “double gaussian” temperature profiles.
Abstract Unstable particles rarely feature in conjunction with integrability in 1+1D quantum field theory. However, the family of homogenous sine-Gordon models provides a rare example where both stable and unstable bound states are present in the spectrum whilst the scattering matrix is diagonal and solves the usual bootstrap equations. In the standard scattering picture, unstable particles result from complex poles of the S-matrix located in the unphysical sheet of rapidity space. Since they are not part of the asymptotic spectrum, their presence is only felt through the effect they have on physical quantities associated either to the theory as a whole (i.e. scaling functions, correlation functions) or to the stable particles themselves (i.e. energy/particle density). In two recent publications, the effect of unstable particles in different out-of-equilibrium settings has been studied. It has been shown that their presence is associated with specific signatures in many quantities of physical interest. A good way to select those quantities is to adopt the generalised hydrodynamic approach and to consider the effective velocities and particle densities of the stable particles in the theory. For an initial state given by a spacial gaussian profile of temperatures peaked at the origin, time evolution gives rise to particle and spectral particle densities that exhibit hallmarks of the creation and decay of unstable particles. While these signatures have been observed numerically elsewhere, this paper explores their quantitative and qualitative dependence on the parameters of the problem. We also consider other initial states characterised by “inverted gaussian” and “double gaussian” temperature profiles.
In the context of quantum field theory (QFT), unstable particles are associated with complex-valued poles of two-body scattering matrices in the unphysical sheet of rapidity space. The Breit-Wigner formula relates this pole to the mass and life-time of the particle, observed in scattering events. In this paper, we uncover new, dynamical signatures of unstable excitations and show that they have a strong effect on the non-equilibrium properties of QFT. Focusing on a 1+1D integrable model, and using the theory of Generalized Hydrodynamics, we study the formation and decay of unstable particles by analysing the release of hot matter into a low-temperature environment. We observe the formation of tails and the decay of the emitted nonlinear waves, in sharp contrast to the situation without unstable excitations. We also uncover a new phenomenon by which a wave of a stable population of unstable particles may persist without decay for long times. We expect these signatures of the presence of unstable particles to have a large degree of universality. Our study shows that the out-of-equilibrium dynamics of many-body systems can be strongly affected not only by the spectrum, but also by excitations with finite life-times.
This thesis presents theoretical groundwork for the investigation of particular phenomena of instability and decay in out-of-equilibrium many body systems. By employing mathematical methods of integrability, we succeed in gaining new insights into problems not traditionally associated with an integrable realm. The family of homogeneous sine-Gordon models provides a rare example of an integrable quantum field theory where both stable and unstable excitations are present in the spectrum. We studied the effect of unstable particles in different out-of-equilibrium settings and have shown that their presence is associated with specific signatures in many quantities of physical interest. Adopting the generalized hydrodynamic approach, we investigated the non-equilibrium dynamics following a quench and observed hallmarks of the creation and decay of unstable particles. Furthermore, we explored in considerable detail their quantitative and qualitative dependence on the parameters of the problem. Decay processes due to environmental interactions are an experimentally relevant problem, yet the theory of open systems is substantially less developed than for their closed counterparts. We concentrate on Markovian open quantum systems described by a Lindblad time evolution equation and design a framework for analytic investigation of Lindblad dynamics via establishing a connection with integrability. We identify a number of Lindblad equations that can be mapped onto non-Hermitian interacting Yang-Baxter integrable models. The key ingredient of the proposed map is the structural similarity between the operators considered. We present examples of mappings between integrable Hamiltonians and Lindblad generators and underline several models of physical interest which can be investigated within this framework. By employing Bethe ansatz techniques, we study the dynamics of some of these models.
Abstract The generalized hydrodynamic (GHD) approach has been extremely successful in describing the out-of-equilibrium properties of a great variety of integrable many-body quantum systems. It naturally extracts the large-scale dynamical degrees of freedom of the system, and is thus a particularly good probe for emergent phenomena. One such phenomenon is the presence of unstable particles, traditionally seen via special analytic structures of the scattering matrix. Because of their finite lifetime and energy threshold, these are especially hard to study. In this paper we apply the GHD approach to a model possessing both unstable excitations and quantum integrability. The largest family of relativistic integrable quantum field theories known to have these features are the homogeneous sine-Gordon models. We consider the simplest non-trivial example of such theories and investigate the effect of an unstable excitation on various physical quantities, both at equilibrium and in the non-equilibrium state arising from the partitioning protocol. The hydrodynamic approach sheds new light onto the physics of the unstable particle, going much beyond its definition via the analytic structure of the scattering matrix, and clarifies its effects both on the equilibrium and out-of-equilibrium properties of the theory. Crucially, within this dynamical perspective, we identify unstable particles as finitely-lived bound states of co-propagating stable particles of different types, and observe how stable populations of unstable particles emerge in large-temperature thermal baths.
We elucidate the physical nature of ghosts above the multi-particle threshold by contrasting them with unstable particles in quantum field theory. We first consider the asymptotic formulation, where ordinary positive-norm one-particle states can be unstable and decay, whereas ghosts survive asymptotically without decaying, yet admit no particle interpretation due to interference with the multi-particle component which masks the negative-norm one-particle state. This distinction originates from two different analytic structures of the dressed propagator, whose complex conjugate poles lie on the first or second Riemann sheet in the ghost or ordinary case, respectively. Ghost resonances are, in principle, phenomenologically distinguishable from ordinary ones, being narrower and exhibiting weaker interference between positive- and negative-energy peaks. We then formulate the quantum field theory in a finite interval of time and, working within a suitable approximation for the dressed propagator, find that finite-time effects amplify differences in the resonant behavior and give rise to new features, such as higher peaks in ghost resonances. Distinct temporal regimes are also identified: for times shorter than the inverse width, an approximate free-particle description is valid; at later times interactions and interference dominate, leading to decay or multi-particle masking. This study supports the absence of freely propagating ghost particles in the asymptotic limit.
In this thesis we study three examples of interacting many-body systems undergoing a non equilibrium time evolution. Firstly we consider the time evolution in an integrable system: the sine-Gordon field theory in the repulsive regime. We will focus on the one point function of the semi-local vertex operator eiβφ(x)/2 on a specific class of initial states. By analytical means we show that the expectation value considered decays exponentially to zero at late times and we determine the decay time. The method employed is based on a form-factor expansion and uses the "Representative Eigenstate Approach" of Ref. [73] (a.k.a. "Quench Action"). In a second example we study the time evolution in models close to "special" integrable points characterised by hidden symmetries generating infinitely many local conservation laws that do not commute with one another, in addition to the infinite commuting family implied by integrability. We observe that both in the case where the perturbation breaks the integrability and when it breaks only the additional symmetries maintaining integrability, the local observables show a crossover behaviour from an initial to a final quasi stationary plateau. We investigate a weak coupling limit, identify a time window in which the effects of the perturbations become significant and solve the time evolution through a mean-field mapping. As an explicit example we study the XYZ spin-1/2 chain with additional perturbations that break integrability. Finally, we study the effects of integrability breaking perturbations on the non-equilibrium evolution of more general many-particle quantum systems, where the unperturbed integrable model is generic. We focus on a class of spinless fermion models with weak interactions. We employ equation of motion techniques that can be viewed as generalisations of quantum Boltzmann equations. We benchmark our method against time dependent density matrix renormalisation group computations and find it to be very accurate as long as interactions are weak. For small integrability breaking, we observe robust prethermalisation plateaux for local observables on all accessible time scales. Increasing the strength of the integrability breaking term induces a "drift" away from the prethermalisation plateaux towards thermal behaviour. We identify a time scale characterising this crossover.
We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the structure of the resulting coupled integral equations encoded in terms of graphical diagrams. The resulting framework is applied to derive results for the Drude weights of charge and energy. Quantities associated with the charge universally have fractal dependence on the coupling, which is notably absent from those associated with energy, a feature explained by the different roles played by reflective scattering in transporting these quantities. We then present far-from-equilibrium results, including explicit time evolution starting from bipartite initial states and dynamical correlation functions. Our framework can be applied to explore numerous other aspects of non-equilibrium dynamics, which opens the way to a wide array of theoretical studies and potential novel experimental predictions.