Quantum Brownian motion of multipartite systems and their entanglement dynamics

We solve the model of N quantum Brownian oscillators linearly coupled to an environment of quantum oscillators at finite temperature, with no extra assumptions about the structure of the system-environment coupling. Using a compact phase-space formalism, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. Since our framework is intrinsically nonperturbative, we are able to analyze the entanglement dynamics of two oscillators coupled to a common scalar field in previously unexplored regimes, such as off resonance and strong coupling.Comment: 10 pages, 6 figure

Initial state preparation with dynamically generated system-environment correlations

The dependence of the dynamics of open quantum systems upon initial correlations between the system and environment is an utterly important yet poorly understood subject. For technical convenience most prior studies assume factorizable initial states where the system and its environments are uncorrelated, but these conditions are not very realistic and give rise to peculiar behaviors. One distinct feature is the rapid build up or a sudden jolt of physical quantities immediately after the system is brought in contact with its environments. The ultimate cause of this is an initial imbalance between system-environment correlations and coupling. In this note we demonstrate explicitly how to avoid these unphysical behaviors by proper adjustments of correlations and/or the coupling, for setups of both theoretical and experimental interest. We provide simple analytical results in terms of quantities that appear in linear (as opposed to affine) master equations derived for factorized initial states.Comment: 6 pages, 2 figure

Toldo urbano: Posibilidades de reducción de la demanda de refrigeración

As a result of the current economic and energy crisis, it has become necessary to rethink urban planning, starting from a global concept of efficiency and considering buildings not as isolated entities, but as part of an urban system, which consumes energy on a much larger scale. The connection between urban morphology and microclimate is a widely discussed question, including issues like the urban heat island phenomenon or outdoor comfort in open spaces. However, there is still a lot of work to be done regarding the influence of these microclimatic variations on building energy consumption. In that sense, would it be possible to apply efficient measures of microclimate modification on an urban scale to increase comfort levels in public spaces while at the same time, reducing building consumption? This paper focuses on urban canopy shading. Its effectiveness as a shading device and its capability to improve outdoor climate in areas with an excess of solar radiation is widely demonstrated. In this case, its effect on indoor climate of is evaluated. The case study is located in Cordoba (Spain), as an example of a climate with a hot and dry summer (according to CTE, level 4). A complete street canyon model has been created. Two buildings, one on each side of the street canyon, have been tested using an energy simulation software (Design Builder). Model features and simulation settings correspond to real values. Urban canopy shading effectiveness has been analyzed according to cooling demand decrease, taking into account both buildings. Spatial factors (street orientation, width-height ratio, windows-opaque ratio) and material factors (U-values and skin mass, % obstruction) have been considered. Results show 18% to 45% cooling demand decrease due to the canopy shading. Spatial factors are much more relevant than material factors: windows-opaque ratio is a determining factor, in contrast to mass and U-values. This study shows the importance of evaluating both urban facades, which means working from an urban perspective beyond the local scale of a single building.El contexto de crisis económica y energética en que nos encontramos, hace necesario repensar la forma de planificar la ciudad partiendo de un concepto global de eficiencia y entendiendo los edificios no como entes aislados que consumen energía, sino como parte de un sistema, consumidor una escala mucho mayor. La relación entre morfología urbana y el microclima es una cuestión ampliamente tratada, abordándose el fenómeno isla de calor o el confort en espacios urbanos. Sin embargo, en cuanto a la influencia de estas variaciones microclimáticas sobre el consumo energético del edificio, aún queda mucho por hacer. En esta línea, nos planteamos: ¿sería posible implantar estrategias de modificación del microclima a escala urbana, que aumenten los niveles de confort en exterior y, simultáneamente disminuyan el consumo de los edificios? En este artículo se analiza el caso del toldo urbano. Su eficacia como elemento de sombra, y su capacidad de mejorar las condiciones exteriores en climas con exceso de radiación solar, está ampliamente demostrada. En esta ocasión, nos centramos en su repercusión sobre el ambiente interior en edificios residenciales. El caso de estudio se localiza en Córdoba (España), ejemplo de clima con verano cálido y seco (según CTE, severidad 4). Se ha creado un modelo de cañón urbano, en cuya parte central se ubican los dos edificios (uno a cada lado de la calle) objeto de simulación energética con Design Builder. Las características del modelo y simulación, responden a condiciones similares a las edificaciones residenciales del entorno. La efectividad del toldo se ha analizado en base a la disminución de demanda de refrigeración que genera, teniendo en cuenta ambos edificios. Se han considerado tanto variables espaciales (orientación de la calle, proporción ancho-alto, % de hueco en fachadas) como materiales (Transmitancia y masa de los cerramientos,% obstrucción solar del toldo). Los resultados reflejan reducciones de demanda entre el 18 y el 45% y una mayor importancia de las variables espaciales frente a las materiales. El % de hueco en fachada se muestra como parámetro de gran relevancia, en contraposición a la masa y la transmitancia. Se concluye que el análisis debe efectuarse considerando las dos fachadas urbanas en su totalidad, es decir, partiendo de una perspectiva urbana que trasciende de la escala local de edificio

Non-Equilibrium Fluctuation-Dissipation Inequality and Non-Equilibrium Uncertainty Principle

The fluctuation-dissipation relation is usually formulated for a system interacting with a heat bath at finite temperature in the context of linear response theory, where only small deviations from the mean are considered. We show that for an open quantum system interacting with a non-equilibrium environment, where temperature is no longer a valid notion, a fluctuation-dissipation inequality exists. Clearly stated, quantum fluctuations are bounded below by quantum dissipation, whereas classically the fluctuations can be made to vanish. The lower bound of this inequality is exactly satisfied by (zero-temperature) quantum noise and is in accord with the Heisenberg uncertainty principle, both in its microscopic origins and its influence upon systems. Moreover, it is shown that the non-equilibrium fluctuation-dissipation relation determines the non-equilibrium uncertainty relation in the weak-damping limit.Comment: 6 pages, no figure

The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis

We provide an in-depth and thorough treatment of the validity of the rotating-wave approximation (RWA) in an open quantum system. We find that when it is introduced after tracing out the environment, all timescales of the open system are correctly reproduced, but the details of the quantum state may not be. The RWA made before the trace is more problematic: it results in incorrect values for environmentally-induced shifts to system frequencies, and the resulting theory has no Markovian limit. We point out that great care must be taken when coupling two open systems together under the RWA. Though the RWA can yield a master equation of Lindblad form similar to what one might get in the Markovian limit with white noise, the master equation for the two coupled systems is not a simple combination of the master equation for each system, as is possible in the Markovian limit. Such a naive combination yields inaccurate dynamics. To obtain the correct master equation for the composite system a proper consideration of the non-Markovian dynamics is required.Comment: 17 pages, 0 figures

Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field

We derive the stochastic equations and consider the non-Markovian dynamics of a system of multiple two-level atoms in a common quantum field. We make only the dipole approximation for the atoms and assume weak atom-field interactions. From these assumptions we use a combination of non-secular open- and closed-system perturbation theory, and we abstain from any additional approximation schemes. These more accurate solutions are necessary to explore several regimes: in particular, near-resonance dynamics and low-temperature behavior. In detuned atomic systems, small variations in the system energy levels engender timescales which, in general, cannot be safely ignored, as would be the case in the rotating-wave approximation (RWA). More problematic are the second-order solutions, which, as has been recently pointed out, cannot be accurately calculated using any second-order perturbative master equation, whether RWA, Born-Markov, Redfield, etc.. This latter problem, which applies to all perturbative open-system master equations, has a profound effect upon calculation of entanglement at low temperatures. We find that even at zero temperature all initial states will undergo finite-time disentanglement (sometimes termed "sudden death"), in contrast to previous work. We also use our solution, without invoking RWA, to characterize the necessary conditions for Dickie subradiance at finite temperature. We find that the subradiant states fall into two categories at finite temperature: one that is temperature independent and one that acquires temperature dependence. With the RWA there is no temperature dependence in any case.Comment: 17 pages, 13 figures, v2 updated references, v3 clarified results and corrected renormalization, v4 further clarified results and new Fig. 8-1

Dissipation, noise and vacuum decay in quantum field theory

We study the process of vacuum decay in quantum field theory focusing on the stochastic aspects of the interaction between long and short-wavelength modes. This interaction results in a diffusive behavior of the reduced Wigner function describing the state of the long-wavelength modes, and thereby to a finite activation rate even at zero temperature. This effect can make a substantial contribution to the total decay rate.Comment: 5 page

Cell size distribution in a random tessellation of space governed by the Kolmogorov-Johnson-Mehl-Avrami model: Grain size distribution in crystallization

The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions

Backreaction from non-conformal quantum fields in de Sitter spacetime

We study the backreaction on the mean field geometry due to a non-conformal quantum field in a Robertson-Walker background. In the regime of small mass and small deviation from conformal coupling, we compute perturbatively the expectation value of the stress tensor of the field for a variety of vacuum states, and use it to obtain explicitly the semiclassical gravity solutions for isotropic perturbations around de Sitter spacetime, which is found to be stable. Our results show clearly the crucial role of the non-local terms that appear in the effective action: they cancel the contribution from local terms proportional to the logarithm of the scale factor which would otherwise become dominant at late times and prevent the existence of a stable self-consistent de Sitter solution. Finally, the opposite regime of a strongly non-conformal field with a large mass is also considered.Comment: 31 page