We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one-dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by particle production at a constant rate which we derive analytically. The produced particles can be physically interpreted according to a semiclassical picture and the state reached in the long time limit can be classified as a non-equilibrium-steady-state. Such a quantum quench can be used in order to observe macroscopic effects of Klein tunneling in transport, with potential implementations with current experimental setups.
We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one-dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by particle production at a constant rate which we derive analytically. The produced particles can be physically interpreted according to a semiclassical picture and the state reached in the long time limit can be classified as a non-equilibrium-steady-state. Such a quantum quench can be used in order to observe macroscopic effects of Klein tunneling in transport, with potential implementations with current experimental setups.
We study quantum transport after an inhomogeneous quantum quench in a free fermion lattice system in the presence of a localised defect. Using a new rigorous analytical approach for the calculation of large time and distance asymptotics of physical observables, we derive the exact profiles of particle density and current. Our analysis shows that the predictions of a semiclassical approach that has been extensively applied in similar problems match exactly with the correct asymptotics, except for possible finite distance corrections close to the defect. We generalise our formulas to an arbitrary non-interacting particle-conserving defect, expressing them in terms of its scattering properties.
We construct non-equilibrium steady states in the Klein–Gordon theory in arbitrary space dimension d following a local quench. We consider the approach where two independently thermalized semi-infinite systems, with temperatures and , are connected along a -dimensional hypersurface. A current-carrying steady state, described by thermally distributed modes with temperatures and for left and right-moving modes, respectively, emerges at late times. The non-equilibrium density matrix is the exponential of a non-local conserved charge. We obtain exact results for the average energy current and the complete distribution of energy current fluctuations. The latter shows that the long-time energy transfer can be described by a continuum of independent Poisson processes, for which we provide the exact weights. We further describe the full time evolution of local observables following the quench. Averages of generic local observables, including the stress-energy tensor, approach the steady state with a power-law in time, where the exponent depends on the initial conditions at the connection hypersurface. We describe boundary conditions and special operators for which the steady state is reached instantaneously on the connection hypersurface. A semiclassical analysis of freely propagating modes yields the average energy current at large distances and late times. We conclude by comparing and contrasting our findings with results for interacting theories and provide an estimate for the timescale governing the crossover to hydrodynamics. As a modification of our Klein–Gordon analysis we also include exact results for free Dirac fermions.
We explore the dynamics of relativistic quantum waves in a potential step by using an exact solution to the Klein-Gordon equation with a point-source initial condition. We show that in both the propagation and Klein-tunneling regimes, the zitterbewegung effect manifests itself as a series of quantum beats of the particle density in the long-time limit. We demonstrate that the beating phenomenon is characterized by the zitterbewegung frequency and that the amplitude of these oscillations decays as ${t}^{\ensuremath{-}3/2}$. We show that the beating effect also manifests itself in the free Klein-Gordon and Dirac equations within a quantum shutter setup, which involve the dynamics of cutoff quantum states. We also find a time domain where the particle density of the point source is governed by the propagation of a main wavefront, exhibiting an oscillating pattern similar to the diffraction-in-time phenomenon observed in nonrelativistic systems. The relative positions of these wavefronts are used to investigate the time delay of quantum waves in the Klein-tunneling regime. We show that depending on the energy difference E between the source and the potential step, the time delay can be positive, negative, or zero. The latter case corresponds to a super-Klein-tunneling configuration, where E equals half the energy of the potential step.
We study inhomogeneous quantum quenches in the attractive regime of the sine--Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine--Gordon Hamiltonian. Varying either the interaction strength of the sine--Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein--Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine--Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine--Gordon dynamics in arbitrary inhomogeneous settings.
We study inhomogeneous quantum quenches in the attractive regime of the sine-Gordon model. In our protocol, the system is prepared in an inhomogeneous initial state in finite volume by coupling the topological charge density operator to a Gaussian external field. After switching off the external field, the subsequent time evolution is governed by the homogeneous sine-Gordon Hamiltonian. Varying either the interaction strength of the sine-Gordon model or the amplitude of the external source field, an interesting transition is observed in the expectation value of the soliton density. This affects both the initial profile of the density and its time evolution and can be summarised as a steep transition between behaviours reminiscent of the Klein-Gordon, and the free massive Dirac fermion theory with initial external fields of high enough magnitude. The transition in the initial state is also displayed by the classical sine-Gordon theory and hence can be understood by semi-classical considerations in terms of the presence of small amplitude field configurations and the appearance of soliton excitations, which are naturally associated with bosonic and fermionic excitations on the quantum level, respectively. Features of the quantum dynamics are also consistent with this correspondence and comparing them to the classical evolution of the density profile reveals that quantum effects become markedly pronounced during the time evolution. These results suggest a crossover between the dominance of bosonic and fermionic degrees of freedom whose precise identification in terms of the fundamental particle excitations can be rather non-trivial. Nevertheless, their interplay is expected to influence the sine-Gordon dynamics in arbitrary inhomogeneous settings.
Recent experimental advances on ultracold atomic gases and trapped ions have made it possible to simulate exactly solvable quantum systems of interacting particles. In particular, the feasibility of making rapid changes, so-called quantum quenches, to such set-ups has allowed experimentalists to probe non-equilibrium phenomena in closed interacting quantum systems. This, in turn, has spurred a considerable theoretical interest in quantum many-body systems out of equilibrium. In this thesis, we study non-equilibrium properties of quantum many-body systems in the framework of exactly solvable quantum field theory in one spatial dimension. Specific systems include interacting fermions described by the Luttinger model and effective descriptions of spin chains using conformal field theory (CFT). Special emphasis is placed on heat and charge transport, studied from the point of view of quench dynamics, and, in particular, the effects of breaking conformal symmetries on transport properties. Examples include the Luttinger model with non-local interactions, breaking Lorentz and scale invariance, and inhomogeneous CFT, which generalizes standard CFT in that the usual propagation velocity v is replaced by a function v(x) that depends smoothly on the position x, breaking translation invariance. The quench dynamics studied here is for quantum quenches between, in general, different smooth inhomogeneous systems. An example of this is the so-called smooth-profile protocol, in which the initial state is defined by, e.g., smooth inhomogeneous profiles of inverse temperature and chemical potential, and the time evolution is governed by a homogeneous Hamiltonian. Using this protocol, we compute exact analytical results for the full time evolution of the systems mentioned above. In particular, we derive finite-time results that are universal in the sense that the same relations between the non-equilibrium dynamics and the initial profiles hold for any unitary CFT. These results also make clear that heat and charge transport in standard CFT are purely ballistic. Finally, we propose and study an inhomogeneous CFT model with v(x) given by a random function. We argue that this model naturally emerges as an effective description of one-dimensional quantum many-body systems with certain static random impurities. Using tools from wave propagation in random media, we show that such impurities lead to normal and anomalous diffusive contributions to heat transport on top of the ballistic one known from standard CFT.