Time-Dependent Approaches to Open Quantum Systems

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.

Driven quantum systems, described by Hamiltonian Open image in new window where x(t) is a time dependent parameter, are of interest in mesoscopic physics (quantum dots), as well as in nuclear, atomic and molecular physics. Such systems tend to absorb energy. This irreversible effect is known as dissipation. More generally, x may b e a dynamical variable, where the total Hamiltonian is Open image in new window . In such case the interaction of (x, p) with the environmental degrees of freedom (Q, P) leads to dephasing as well as to dissipation. It should be emphasized that even few (Q, P) degrees of freedom can serve as a miniature heat bath, provided they have chaotic dynamics. We shall introduce a general framework for the analysis of dissipation and dephasing, and we shall clarify the tight connection to recent studies of quantum irreversibility (also referred to as “Loschmidt echo” or as the “fidelity” of quantum computation). Specific model systems that will be presented are: particle in a box driven by moving a wall, and particle in a box/ring driven by electro-motive-force. These two examples are related to studies of nuclear friction and mesoscopic conductance. Specific issues to be discussed are the limitations of kinetic theory, the capabilities of linear response theory, and the manifestation of non-perturbative quantum-mechanical effects. In particular we shall explain that random matrix theory and the semiclassical theory lead to different non-perturbative limits.

Time evolution generically entangles a quantum state with environmental degrees of freedom. The resulting increase in entropy changes the properties of that quantum system leading to “aging”. It is interesting to ask if this familiar property also applies to simple, single particle quantum systems such as the decay of a radioactive particle. We propose a test of such aging in an ion clock setup where we probe for temporal changes to the energies of the electronic state of an ion containing a radioactive nucleus. Such effects are absent in standard quantum mechanics and this test is thus a potent null test for violations of quantum mechanics. As a proof of principle, we show that these effects exist in causal non-linear modifications of quantum mechanics.

The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body systems, to applications in condensed matter theory, quantum transport, quantum chemistry and quantum information. In close analogy to a classical Markov process, the interaction of an open quantum system with a noisy environment is often modelled by a dynamical semigroup with a generator in Lindblad form, which describes a memoryless dynamics leading to an irreversible loss of characteristic quantum features. However, in many applications open systems exhibit pronounced memory effects and a revival of genuine quantum properties such as quantum coherence and correlations. Here, recent results on the rich non-Markovian quantum dynamics of open systems are discussed, paying particular attention to the rigorous mathematical definition, to the physical interpretation and classification, as well as to the quantification of memory effects. The general theory is illustrated by a series of examples. The analysis reveals that memory effects of the open system dynamics reflect characteristic features of the environment which opens a new perspective for applications, namely to exploit a small open system as a quantum probe signifying nontrivial features of the environment it is interacting with. This article further explores the various physical sources of non-Markovian quantum dynamics, such as structured spectral densities, nonlocal correlations between environmental degrees of freedom and correlations in the initial system-environment state, in addition to developing schemes for their local detection. Recent experiments on the detection, quantification and control of non-Markovian quantum dynamics are also discussed.

The effect of noise on quantum teleportation of a spin-$\frac{1}{2}$ state using an entangled pair is studied. We calculate the time evolution of the density matrix of the three involved particles due to their coupling with the environmental degrees of freedom. We evaluate the fidelity of transmission as a function of time under a variety of conditions and compare the fidelities obtained for different entangled states. We find that for a generic coupling to environment, use of the singlet state for the entangled pair yields the highest fidelity in noisy conditions.

We develop a method to study quantum impurity models, small interacting quantum systems bilinearly coupled to an environment, in the presence of an additional Markovian quantum bath, with a generic nonlinear coupling to the impurity. We aim at computing the evolution operator of the reduced density matrix of the impurity, obtained after tracing out all the environmental degrees of freedom. First, we derive an exact real-time hybridization expansion for this quantity, which generalizes the result obtained in the absence of the additional Markovian dissipation and which could be amenable to stochastic sampling through diagrammatic Monte Carlo. Then, we obtain a Dyson equation for this quantity and we evaluate its self-energy with a resummation technique known as the noncrossing approximation. We apply this novel approach to a simple fermionic impurity coupled to a zero temperature fermionic bath and in the presence of Markovian pump, losses, and dephasing.

Photosynthetic processes are driven by sunlight. Too little of it and the photosynthetic machinery cannot produce the reductive power to drive the anabolic pathways. Too much sunlight and the machinery can get damaged. In higher plants, the major Light Harvesting Complex (LHCII) efficiently absorbs the light energy, but can also dissipate it when in excess (quenching). In order to study the dynamics related to the quenching process but also the exciton dynamics in general, one needs to accurately determine the so-called spectral density which describes the coupling between the relevant pigment modes and the environmental degrees of freedom. To this end, Born–Oppenheimer molecular dynamics simulations in a quantum mechanics/molecular mechanics (QM/MM) fashion utilizing the density functional based tight binding (DFTB) method have been performed for the ground state dynamics. Subsequently, the time-dependent extension of the long-range-corrected DFTB scheme has been employed for the excited state calculations of the individual chlorophyll-a molecules in the LHCII complex. The analysis of this data resulted in spectral densities showing an astonishing agreement with the experimental counterpart in this rather large system. This consistency with an experimental observable also supports the accuracy, robustness, and reliability of the present multi-scale scheme. In addition, the resulting spectral densities and site energies were used to determine the exciton transfer rate within a special pigment pair consisting of a chlorophyll-a and a carotenoid molecule which is assumed to play a role in the balance between the light harvesting and quenching modes.

Before starting on some remarks summarizing the meeting we have just completed, I would like to say a few words about one of the organizers. As we heard at the conference, Jack Leigh of the Australian National University has decided to retire in the very near future. Jack was a student of John Newton's at Manchester and then a postdoc in Berkeley before coming to Canberra where he has remained ever since. Jack's work has been characterized by an attention to detail and a critical examination of the physics, of which we have seen many examples at this meeting. This thorough approach has led us to a re-evaluation of many of the basic ideas of nuclear dynamics, an area which still holds some surprises and new aspects. I am sure we all wish him well in his retirement and, although he claims otherwise, I find it hard to believe that he will be away from the lab for long!

Fluid-Structure Coupling Effects on the Dynamic Response of Pump-Turbine Guide Vanes

The effects of higher-order coupling of surface vibrations to the relative motion on heavy-ion fusion reactions at near-barrier energies are investigated. The coupled-channels equations are solved to all orders, and also in the linear and the quadratic-coupling approximations. It is shown that the shape of fusion-barrier distributions and the energy dependence of the average angular momentum of the compound nucleus can significantly change when the higher-order couplings are included. The role of octupole vibrational excitation of in the fusion reaction is also discussed using the all-order coupled-channels equations.

In this contribution we discuss the most significant benefits and drawbacks of the alternative time‐independent (TI) and time‐dependent (TD) approaches to the calculation of absorption spectra of molecules in solutions. Eigenstate‐free TD methods are in principle the most suitable route to face with the calculation of optical spectra in nonadiabatic systems, most of all in presence of conical intersections easily accessible from the Franck–Condon region. However, here we show that, in selected cases, a combined strategy that adopts TD methods to assess the impact of nonadiabatic couplings on the spectrum and subsequently applies TI methods to include all the degrees of freedom can reveal very convenient. Such a combined TD/TI strategy has been applied to the calculation of the spectrum of Uracil and 5Fluoro‐Uracil in acetonitrile. TD studies on reduced dimensionality diabatic models indicate that nonadiabatic effects are moderate and are not the main origin of the diffuse spectral shapes observed in experiments. Subsequent full‐coordinate TI calculations allow assigning this feature to intrinsic characteristics of a ππ* excitation of a small molecular ring structure. This latter introduces remarkable deformation in all the ring structure thus inducing a FC activity in many molecular normal modes both due to displacements of the equilibrium structures and to Duschinsky mixings of the normal coordinates. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution. Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Building pounding philosophy is the collision of adjacent buildings when earthquake take place and buildings show lateral movement. Providing suitable separation distance, impact force precludes and reduces the failure of construction elements. In this paper, building pounding between two reinforced concrete buildings with insufficient gap size is numerically investigated in order to study the impact force during seismic excitations. For this challenge, two to three story concrete buildings are modeled by finite element software. On the other hand, two mathematic models of RC buildings with lumped masses are considered to get the results of pounding and effect of impact on structural behavior. A mathematic program is used based on single degree-of-freedom (SDOF) equations to analyze the failure of models. Since calculation of impact forces depends significantly on link element assigned between two bodies, special link element is utilized. Used link element between two buildings is included in a spring with high stiffness and a viscous impact dashpot, which were located parallel in order to absorb the energy loss during impact. Finally, a new equation of motion is suggested to calculate the impact force. The accuracy of suggested equation is confirmed by energy equation. Key words: Building pounding, impact, dissipated energy, finite element.

Contact interfaces, particularly as found in jointed structures, are potential sources of energy dissipation, wear, and damage. Consequently, accurate analysis of structures with contact interfaces is paramount for assessing functionality and potential failure mechanisms. Numerical and experimental analyses of a jointed structure, however, are endeavors that require a significant investment of time and resources. The strategy employed for the analysis of the joint depends typically upon whether energy dissipation is a positive or negative feature for a joint within a larger system. In this chapter, a technique for efficiently calculating the shakedown limit of coupled, discrete frictional systems with a large number of degrees of freedom (DOFs) is examined. This calculation is applied to a complete contact problem between a square punch and an elastically similar half-plane, and the influence of initial conditions on steady-state energy dissipation is investigated. The calculated value of the shakedown limit is then compared to a series of transient simulations that were run until a steady state was reached. These results demonstrate that the dissipative properties of coupled complete contacts can be highly dependent on the initial residual slip displacement state.

The coupled-channels method has been a standard tool in analyzing heavy-ion fusion reactions at energies around the Coulomb barrier. We investigate three simplifications usually adopted in the coupled-channels calculations. These are i) the exclusion of non-collective excitations, ii) the assumption of coordinate independent coupling strengths, and iii) the harmonic oscillator approximation for multi-phonon excitations. In connection to the last point, we propose a novel microscopic method based on the beyond-mean-field approach in order to take into account the anharmonic effects of collective vibrations.