We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered Hamiltonian, with spacetime-varying parameter values drawn from distributions that are generically neither flat nor Gaussian. This class of scenarios is a natural extension of those where a fully non-dynamical environmental degree of freedom determines a universal coupling constant for the system. Using a family of quasi-exactly solvable anharmonic oscillators, we consider environmental ground states of nonlinearly coupled degrees of freedom, unrestricted by a weak coupling expansion, which include strongly quantum non-Gaussian states. We derive the properties of distributions for both quadrature and photon number measurements. Measurement-induced disorder of this kind is likely realizable in laboratory quantum systems and, given a notion of naturally occurring measurement, suggests a new class of scenarios for the dynamics of quantum systems in particle physics and cosmology.
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered Hamiltonian, with spacetime-varying parameter values drawn from distributions that are generically neither flat nor Gaussian. This class of scenarios is a natural extension of those where a fully non-dynamical environmental degree of freedom determines a universal coupling constant for the system. Using a family of quasi-exactly solvable anharmonic oscillators, we consider environmental ground states of nonlinearly coupled degrees of freedom, unrestricted by a weak coupling expansion, which include strongly quantum non-Gaussian states. We derive the properties of distributions for both quadrature and photon number measurements. Measurement-induced disorder of this kind is likely realizable in laboratory quantum systems and, given a notion of naturally occurring measurement, suggests a new class of scenarios for the dynamics of quantum systems in particle physics and cosmology.
A one-dimensional quantum oscillator is monitored by taking repeated position measurements. As a first contribution, it is shown that, under a quantum nondemolition measurement scheme applied to a system initially at the ground state, (i) the observed sequence of measurements (quantum tracks) corresponding to a single experiment converges to a limit point, and that (ii) the limit point is random over the ensemble of the experiments, being distributed as a zero-mean Gaussian random variable with a variance at most equal to the ground-state variance. As a second contribution, the richer scenario where the oscillator is coupled with a frozen (i.e., at the ground state) ensemble of independent quantum oscillators is considered. A sharply different behavior emerges: under the same measurement scheme, here we observe that the measurement sequences are essentially divergent. Such a rigorous statistical analysis of the sequential measurement process might be useful for characterizing the main quantities that are currently used for inference, manipulation, and monitoring of many quantum systems. Several interesting properties of the quantum tracks evolution, as well as of the associated (quantum) threshold crossing times, are discussed and the dependence upon the main system parameters (e.g., the choice of the measurement sampling time, the degree of interaction with the environment, the measurement device accuracy) is elucidated. At a more fundamental level, it is seen that, as an application of basic quantum mechanics principles, a sharp difference exists between the intrinsic randomness unavoidably present in any quantum system, and the extrinsic randomness arising from the environmental coupling, i.e., the randomness induced by an external source of disturbance.
In this thesis, we discuss aspects of the simulation, characterisation, and control of the dynamics of open quantum systems. The latter are systems governed by quantum mechanical laws and interacting with an environment, which is typically much larger than the system itself. According to the standard approach, one is usually able to perform a suitable average over the environmental degrees of freedom, resulting in an effective description of the main system dynamics, which accounts for the effects of the interaction with the surroundings. In standard scenarios, usually studied within the so-called Born-Markov approximation, the system-environment coupling is weak and such that we can perform a neat separation of timescales: the environmental dynamics is assumed to be fast compared to the typical evolution timescale of the system of interest. However, nowadays we are able to inspect physical scenarios where the usual Born-Markov approximation breaks down: the interaction between system and environment can be strong, likely leading to non-negligible memory (non-Markovian) effects. In this work, we discuss some instances in which we cannot work in the standard Born-Markov regime. We introduce and analyse some numerical and analytical techniques to characterise and simulate non-standard scenarios. We show that, even in the Markovian regime, the traditional formulation of thermodynamic irreversibility shows flaws and inconsistencies. We thus use phase-space methods to assess the role of initial correlations shared by the two parties of a bipartite harmonic system in the entropy production rate, including non-Markovian effects. Furthermore, we show that certain interactions enable to redraw the boundaries between the system and the environment in an effective manner, resulting in a new picture where the system degrees of freedom are augmented, while the residual environment is rearranged in such a way that the Born-Markov approximation is recovered. This analytical technique, known as reaction coordinate mapping approach, is employed in this work to show that, upon an accurate choice of the parameter regime, a spin-boson model can serve as a quantum analogue simulator of non-Markovian multiphoton Jaynes-Cummings models. These systematic studies shed light on the thermodynamic characterisation of open quantum systems, as well as on their numerical simulation.
We study quantum quenches in two-dimensional lattice gauge theories with fermions coupled to dynamical Z2 gauge fields. Through the identification of an extensive set of conserved quantities, we propose a generic mechanism of charge localization in the absence of quenched disorder both in the Hamiltonian and in the initial states. We provide diagnostics of this localization through a set of experimentally relevant dynamical measures, entanglement measures, as well as spectral properties of the model. One of the defining features of the models that we study is a binary nature of emergent disorder, related to Z2 degrees of freedom. This results in a qualitatively different behavior in the strong disorder limit compared to typically studied models of localization. For example, it gives rise to a possibility of a delocalization transition via a mechanism of quantum percolation in dimensions higher than 1D. We highlight the importance of our general phenomenology to questions related to dynamics of defects in Kitaev's toric code, and to quantum quenches in Hubbard models. While the simplest models we consider are effectively noninteracting, we also include interactions leading to many-body localizationlike logarithmic entanglement growth. Finally, we consider effects of interactions that generate dynamics for conserved charges, which gives rise to only transient localization behavior, or quasi-many-body localization.
In this work we consider several exactly solvable models of magnetic impurities in critical quantum antiferromagnetic spin chains and multichannel Kondo impurities. Their ground-state properties are studied, and the finite set of nonlinear integral equations which exactly describe the thermodynamics of the models is constructed. We obtain several analytical low-energy expressions for the temperature, magnetic field, and frequency dependences of important characteristics of exactly solvable disordered quantum spin models and disordered multichannel Kondo impurities with essential many-body interactions. We show that the only low-energy parameter that gets renormalized is the velocity of the low-lying excitations (or the effective crossover scale connected with each impurity); the others appear to be universal. In our study several kinds of strong disorder important for experiments were used. Some of them produce low divergences in certain characteristics of our strongly disordered critical systems (compared with finite values for the homogeneous case or a single impurity). For weak disorder, or for narrow distributions of the local Kondo temperatures, our exact results reveal the presence of Kondo screening of disordered ensembles of magnetic impurities by low-lying excitations of the host. We point out that our results qualitatively coincide with the data of experiments on real disordered quasi-one-dimensional antiferromagnetic systems and with the similar behavior of some heavy metallic alloys.
Quantum measurement ensembles represent a fundamental aspect of quantum mechanics, where the outcomes of measurements are inherently probabilistic. This paper explores a novel dynamic model for the evolution of these ensembles, emphasizing the influence of inherent stochasticity. We introduce a model that explicitly incorporates a measure of 'system' evolution, driving the probabilistic outcomes through a dynamic ensemble evolution equation. This approach offers a significant departure from traditional methods, which frequently treat measurement outcomes as fixed, enabling a more nuanced representation of quantum phenomena.
Interaction between a quantum system and its environment can be often regarded as a measurement, in the course of which one of the system observables influences the evolution of the external degrees of freedom and is thus ''monitored'' by the environment. The resulting loss of quantum coherence erases part of the density matrix responsible for the correlations between the eigenstates of the monitored observable. This mechanism is very efficient even in the limit of weak coupling. Indeed, the classical limit of quantum theory---that is, both classically reversible equations of motion and classical states (trajectories in phase space rather than their superpositions) can be naturally attained when both the coupling strength and the Planck constant simultaneously tend to zero. Transition from quantum to classical in the inflationary cosmological models can be justified in the framework of environment induced superselection. 24 refs., 3 figs.