Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green’s function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent. The double-well potential is one of the simplest and best understood problems in modern quantum mechanics. Its utility is likewise unparalleled. Potential applications of double-well devices have been noted in Refs. [1-5]. For such devices to be useful, an understanding of the processes which couple the microscopic device to the macroscopic environment is paramount. That is to say, the decoherence processes of such systems must be well understood. To this end, we consider a simple exactly solvable model of two coupled quantum dots. An excellent review of related systems and some approximate solutions are given in Ref. [6]. Each dot is coupled to an environment (a triple-barrier system) as in Fig. 1. The environment consists of a continuum of states, as would be appropriate for a macroscopic lead. Only one state in each quantum dot is considered, which amounts to the assumption that the tunneling parameters connecting our two states to any neglected state are much less than the energy differences with that state. The Hamiltonian of the system can be written as the sum of two terms, H = H0 + Hc. The first term, H0, represents the dynamics of the simple two-state system, H0 = ε1d † 1d1 + ε2d † 2 d2 + V (d† 1d2 + d†
This thesis investigates two thematic lines of research, both underpinned by non-Markovian system-reservoir interactions in quantum optics. The overarching focus is on modelling the open system dynamics in a non-perturbative fashion, broadly on - though not restricted to - instances when the environment is structured. A theory is developed by means of enlarging the open system over environmental degrees of freedom to include memory effects in its dynamics. This is achieved using an established technique that involves mapping a bosonic environment onto a 1D chain of harmonic oscillators. Within this setting, we apply a Heisenberg equation-of-motion approach to derive an exact set coupled differential equations for the open system and a single auxiliary oscillator of the chain. The combined equations are shown to have their interpretation rooted in a quantum Markov stochastic process. Including the auxiliary chain oscillator as part of the original system then enables us to obtain an exact master equation for the enlarged system, avoiding any need for the Born-Markov approximations. Our method is valid for a dissipative two-state system, with cases of multiple excitations and added driving discussed. Separately, we apply the framework of quantum Darwinism to an atom-cavity system, and, subsequently, to a more general multiple-environment model. In both cases, the time-dependent spread of correlations between the open system and fractions of the environment is analysed during the course of the decoherence process. The degree to which information is redundant across different fractions is checked to infer the emergence of classicality. In the second case, we go further and present a decomposition of information in terms of its quantum and classical correlations. A quantitative measure of redundancy is also studied with regard to its ability to witness non-Markovian behaviour. Besides fundamental interest, our results have application to quantum information processing and quantum technologies, keeping in mind the potential beneficial use of non-Markovian effects in reservoir engineering.
Condensed and solid phase environments offer a wide range of controllable interactions for new quantum technologies.Understanding the dynamics of open quantum systems interacting with such complex environments is important for correct modeling of many chemical and physical phenomena and for development of new quantum technologies.The central theme of this thesis is the open system dynamics of a small qua.ntum system coupled to self-interacting chaotic environments.This thesis consists of Lhree related parts.In the first part, a theory predicting open dynamics of a quantum system interacting with chaotic environments is reported.The theory is of a Kraus decomposition form, which is exact for chaotic environments of thermodynamic dimension.Extension of the theory to time-dependent system Hamiltonians is also presented so that it may have practical applications for studies of new quantum technologies.In tbe second part, extensive numerical calculations are performed to obtain the exact quantum dynamic::; for two realistic models of self-int(~ra.ctingenvironments.Both models represent a statistically Hawed isolated quantum computer (QC) core.In the first model, the open dynamics of a quantum-control NOT (CNOT) gate in the pre::;ence of static internal imperfections are invcstigated and internal error sources are identified for a large number of QC configurations.The results indicate that the strong two-body imperfections suppress the interna.! decohcrence and enhance the performancc of the CNOT gate.Moreover, the largest source of error is found to be unitary due to coherent shifting rather than III
Decoherence represents one of the most fundamental problems in quantum mechanics since its birth. Interest in decoherence has been primarily academic until recently when the advances in experimental techniques in different fields of physics such as superconducting quantum interferometers; quantum optics and neutron interferometry sparked the practical interest in this quantum mechanical phenomenon. One particular field where decoherence is of crucial role is quantum computing, where decoherence stands as one of the main obstacles toward realizing practical progress in the field. On the other hand, the ability to manipulate linear superpositions of quantum states is expected to lead to considerable advances in that field. The purpose of this dissertation is to present a study of decoherence in nonlinear quantum systems. We started by studying the coherent superposition of distinct basis states in a single-degree-of-freedom model of SQUID with a variable potential barrier between the basis flux states. We numerically integrated Schrödinger equation of the system. We found that linear superpositions of the basis states, with relatively little residual excitation, can be formed by pulsed modulation of the potential barrier, provided the pulse duration exceeds the period of small oscillations of the flux. Two pulses applied in sequence exhibit strong interference effects, which we propose to use for an experimental determination of the decoherence time in SQUIDS. In addition, we developed, using quantum field theory techniques, a general formalism to study decoherence in a quantum system due to coupling to a non-linear environment. This formalism can be used to investigate decoherence in many of the existing two state quantum systems proposed for quantum computing and reveals important information about them such as decoherence time. Moreover, we used this formalism to compare decoherence induced in a simple two-state quantum system (qubit) for two different initial states of the environment: canonical (fixed temperature) and microcanonical (fixed energy), for the general case of a fully interacting oscillator environment. We found that even a relatively compact oscillator bath (with effective number of degrees of freedom as low as 10), initially in a microcanonical state, will typically cause decoherence almost indistinguishable from that caused by a macroscopic, thermal environment, except possibly at singularities of the environment's specific heat (critical points). In the latter case the precise magnitude of the difference between the canonical and microcanonical results depends on the critical behavior of the dissipative coefficient, characterizing the interaction of the two-state quantum system with the environment.
The interaction of a quantum system with a many degree o ff reedom environment entails damping and the loss of quantum coherence. In these two lectures we focus on two aspects of open quantum system dynamics. First, we present decoherence as a dynamical phenomenon and determine the corresponding time scales, discuss an experiment and the nature of robust states, and mention universal properties of short- time decoherence of macroscopic superpositions. Secondly, in analogy to the classical description of open systems in terms of Langevin equations, we present a stochastic approach to open quantum system dynamics in terms of a stochastic Schrodinger equation. We give a microscopic ¨ derivation that allows us to generalize the stochastic approach to non- Markovian situations. We discuss a convolutionless formulation of our theory and finally, we focus on the quantised version of Brownian motion as an often-employed example.
Important Update on March 9, 2026: In this version, the description of environmental effects has been corrected: they are now properly treated as encapsulated within the effective spectral density of the interfacial defect network D, rather than as direct driving terms. All core results and conclusions remain unchanged, but the physical interpretation is refined to align with the energy distribution framework introduced in Part II of this series. Version 2 This paper is the third in the "Interface-Projected Realism" series. This series of work aims to establish a new theoretical paradigm: Ontologically, replace probabilistic wave function descriptions with deterministic energy flow; Methodologically, redefine physical reality as an interactive whole composed of quantum units (
Q), an interfacial defect network (
D), and bulk channels (
B). In the first work, an exact relationship between energy flow and relaxation rate was established, providing a formal bridge for the paradigm shift. In the second work, the "Energy Distribution Framework" was proposed, demonstrating that dissipation is the deterministic allocation of energy between
Q and
D, and deriving the universal formula for internal dissipation power
Rint=ℏωq[Γ↓⟨n⟩−Γ↑(1−⟨n⟩)], where the relaxation rates are completely determined by the internal structure of
D, revealing the core role of the energy distribution ratio
f. This paper generalizes this new paradigm based on energy distribution from single-body to many-body systems. The core step is to define multiple
Q contacts and their shared
D and
B together as a new, unified composite system. Within this framework, the traditionally complex "many-body correlated dissipation" is clearly interpreted as a macroscopic result of the deterministic flow of energy within this composite system, governed by allocation and transport rules determined by the structure of the
D network. Through rigorous coarse-graining of this overall system, this paper derives the governing equation for the evolution of its internal energy density field
u(r,t)—a classical reaction-diffusion equation:
∂t∂u=Rtotal−γ0(r)u+∇⋅(γ2∇u).Here, the local dissipation rate
γ0(r) and the diffusion coefficient
γ2 are completely determined by the properties of the
D network, corresponding respectively to the spatial distribution of the energy distribution ratio
f from the second paper and the redistribution effect induced by its correlations. This theory is not only logically self-consistent but also provides a unified explanation for multiple cutting-edge experiments. This paper marks that a physical framework based on deterministic energy distribution and transport can now systematically describe many-body correlation phenomena, providing crucial support for the completeness of the new paradigm. \textbf{Keywords}: Interface-Projected Realism; Energy Distribution; Many-Body Systems; Correlated Dissipation; Reaction-Diffusion Equation Version 1 Traditional quantum theory typically attributes energy dissipation to random perturbations from the external environment. Based on the "Interfacial Projected Realism" framework, this work re-examines the nature of energy dissipation from a novel perspective, treating the qubit, the interfacial defect network, and the bulk dissipation channel as a self-contained total system. We first rigorously derive the universal formula for internal dissipation power and the energy distribution ratio
f in single-body quantum systems, and then extend these concepts to many-body systems. Starting from a microscopic Hamiltonian coupling multiple qubits to a common quantized field and employing the Nakajima-Zwanzig projection operator technique, we obtain a universal expression for the energy dissipated from a many-body system to the environment. Applying this result to the specific model of multiple two-level systems coupled to a common bosonic field yields a collective master equation where the dissipation coefficient matrix
Γij encodes all spatial and coupling information. Through systematic coarse-graining, gradient expansion, and semiclassical approximation, we derive for the first time from an energy-distribution perspective a closed set of macroscopic equations for the local system energy density
u(r,t) and the environmental field energy density
U(r,t):
∂t∂u=Rtotal(r,t)−γ0(U)u+∇⋅(γ2(U)∇u)∂t∂U=D∇2U−ΓBU+ρ(r)γ0(U)u Within this framework, the energy distribution ratio
f(r,t)=γ0u/Rtotal emerges naturally as a macroscopic quantity, its physical essence being jointly determined by the system’s microscopic coupling structure (embodied by
Γij) and quantum statistical state. The theory quantitatively explains several long-unexplained anomalous phenomena in cutting-edge experiments, demonstrates strong testability, and lays a solid foundation for exploring deeper connections between energy distribution and macroscopic physics. For the exact mathematical formulation and detailed derivations, please refer to the PDF file.