In this work we study quantum transport phenomena in two different types of systems. The first type corresponds to so-called complex quantum systems, such as chaotic ballistic cavities and disordered quantum wires, which have a complex distribution of energy levels and transmission eigenvalues. This class of system does not admit a simple description in terms of a fixed Hamiltonian, and therefore we will make a statistical approach of its transport properties through Random Matrices Theory. We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of some smooth transitions that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating transitions. The two Bogolyubov de Gennes symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system. The second type of system corresponds to qubits, which, unlike complex systems, can be described by very simple Hamiltonians. In this case, we study the properties of open systems using master equations. We present a study of non-equilibrium thermodynamics of qubit systems submitted to quantum control. More specifically, we performed a comparative study of two types of simple two-level non-interacting quantum transport systems coupled to two bosonic and fermionic reservoirs respectively. Each system is submitted to a Wiseman-Milburn type feedback scheme in the formulation of stochastic thermodynamics. We see the effects of finite temperature and time delay on two specific feedback applications: a heat pump and a purification protocol. We observed a clear signature of the purity of the qubits in the Full Counting Statistics observed in the current flowing through the system.
In this work we study quantum transport phenomena in two different types of systems. The first type corresponds to so-called complex quantum systems, such as chaotic ballistic cavities and disordered quantum wires, which have a complex distribution of energy levels and transmission eigenvalues. This class of system does not admit a simple description in terms of a fixed Hamiltonian, and therefore we will make a statistical approach of its transport properties through Random Matrices Theory. We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of some smooth transitions that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating transitions. The two Bogolyubov de Gennes symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system. The second type of system corresponds to qubits, which, unlike complex systems, can be described by very simple Hamiltonians. In this case, we study the properties of open systems using master equations. We present a study of non-equilibrium thermodynamics of qubit systems submitted to quantum control. More specifically, we performed a comparative study of two types of simple two-level non-interacting quantum transport systems coupled to two bosonic and fermionic reservoirs respectively. Each system is submitted to a Wiseman-Milburn type feedback scheme in the formulation of stochastic thermodynamics. We see the effects of finite temperature and time delay on two specific feedback applications: a heat pump and a purification protocol. We observed a clear signature of the purity of the qubits in the Full Counting Statistics observed in the current flowing through the system.
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.
A central goal in the study of modern condensed matter physics is the characterization of the dynamical properties of quantum systems. Many decades of effort towards this goal, studying a diverse range of (near-equilibrium) quantum matter, from Fermi liquids, to quantum two-level systems, to interacting spin models, and more, has revealed a remarkable pervasiveness of the simple dynamical description of these complex systems in terms of quasi-particles that carry spin, charge, and heat, and that are generally able to equilibrate systems. \n\nThis thesis is an examination of some exceptions to this rule. Specifically, we study a number of instances of quantum matter where equilibration phenomena happens at rather long time scales, or does not occur at all. Particular emphasis is laid on the role of dimensionality, disorder, and dissipation in engendering such novel dynamical behavior.\n\nFirst, we consider non-equilibrium dynamics in one-dimensional quasi-condensates. Low dimensionality inhibits scattering in these systems, and low-energy excitations are long-lived phase fluctuations that exhibit an enriched conformal symmetry. Utilizing this symmetry, we generalize sudden quenches typically used to study non-equilibrium dynamics to quenches along general relativistic and conformal trajectories. Gases never truly equilibrate after such a quench; instead, they evolve into a `prethermal' state with thermal-looking correlations and a chiral asymmetry. \n\nWe then study the problem of the dynamical transition driven by disorder, from an ergodic to a non-ergodic phase, in one-dimensional quantum spin chains. In particular, in XXZ chains with on-site disorder, we find a unique intermediate phase straddling the boundary of the dynamical phase transition, wherein rare-region effects lead to long-time tails in equilibration and vanishing DC conduction before the onset of non-ergodicity. We propose generalizations of such `Griffiths' behavior to arbitrary dimensions. We also study the dynamics of random-bond Heisenberg chains by developing a strong-disorder renormalization group protocol for these systems. We discuss how magnetic noise from such disordered systems contains signatures of their anomalous dynamical properties. \n\nNext, we re-examine the phenomenological theory of two-level systems in amorphous materials in the light of new experimental evidence that these states have large electric/magnetic dipole moments. We propose and justify an interpretation of the model as one of tunneling electrons slowed down by a large phonon drag and discuss the dynamical consequences of such polaronic effects. \n\nFinally, we discuss how magnetic noise measurements can be used to non-invasively access the anomalous properties of systems such as those discussed above. In particular, we examine how scattering properties of isolated magnetic impurities and non-local transport in a variety of two-dimensional materials can be probed experimentally using NV centers as noise magnetometers.
We study the transport properties of generic out-of-equilibrium quantum systems connected to fermionic reservoirs. We develop a perturbation scheme in the inverse system size, named 1/N expansion, to study a large class of out of equilibrium diffusive/ohmic systems. The bare theory is described by a Gaussian action corresponding to a set of independent two level systems at equilibrium. This allows a simple and compact derivation of the diffusive current as a first-order pertubative term. In addition, we obtain exact solutions for a large class of quantum stochastic Hamiltonians (QSHs) with time and space dependent noise, using a self-consistent Born diagrammatic method in the Keldysh representation. We show that these QSHs exhibit diffusive regimes, which are encoded in the Keldysh component of the single particle Green's function. The exact solution for these QSHs models confirms the validity of our system size expansion ansatz, and its efficiency in capturing the transport properties. We consider in particular three fermionic models: (i) a model with local dephasing, (ii) the quantum simple symmetric exclusion process model, and (iii) a model with long-range stochastic hopping. For (i) and (ii) we compute the full temperature and dephasing dependence of the conductance of the system, both for two- and four-points measurements. Our solution gives access to the regime of finite temperature of the reservoirs, which could not be obtained by previous approaches. For (iii), we unveil a ballistic-to-diffusive transition governed by the range and the nature (quantum or classical) of the hopping. As a byproduct, our approach equally describes the mean behavior of quantum systems under continuous measurement.
We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.
The multivariate fluctuation relation is established for the full counting statistics of the energy and particle fluxes across an open quantum system in contact with several reservoirs on the basis of microreversibility The quantum version of the nonequilibrium work fluctuation relation is recovered in the presence of a single reservoir. In the long-time limit, the time-reversal symmetry relation is expressed in terms of the cumulative generating function for the full counting statistics. In systems with independent particles, the symmetry relation can be obtained in the scattering approach for the transport of bosons and fermions. The temporal disorder and its time asymmetry can be characterized by the quantum version of the entropy and coentropy per unit time. Their difference gives the thermodynamic entropy production rate. Furthermore, the stochastic approach is also considered for electron transport in quantum dots, quantum point contacts, and single-electron transistors.
This thesis studies transport properties of low-dimensional quantum spin systems with a particular focus on the transport of heat and spin. While the integrable anisotropic spin-1/2 chain exhibits ballistic transport (finite Drude weights), the numerical results of this work show that heat and spin transport of non-integrable models (spin ladder, frustrated and dimerized chain) is not ballistic, characterized by vanishing Drude weights in the thermodynamic limit. The results for the thermal conductivity of spin ladders are compared to experimental data. For the case of the spin-1/2 Heisenberg chain, this work contains detailed results for the temperature and magnetic field dependence of the Drude weights. Finally, bond-disordered spin systems are considered, namely the spin-1/2 chain and the spin ladder. In the first case, the transport coefficients are computed by means of exact diagonalization and discussed as a function of frequency, temperature, and magnetic field. In the second case, spectral properties of the elementary excitation of disordered spin ladders are analyzed using diagrammatic perturbation theory and numerical techniques.