Area law for fixed points of rapidly mixing dissipative quantum systems

We prove an area law with a logarithmic correction for the mutual information for fixed points of local dissipative quantum system satisfying a rapid mixing condition, under either of the following assumptions: the fixed point is pure, or the system is frustration free.Comment: 17 pages, 1 figure. Final versio

Relaxation and hysteresis near Shapiro resonances in a driven spinor condensate

We study the coherent and dissipative aspects of a driven spin-1 Bose-Einstein condensate (BEC) when the Zeeman energy is modulated around a static bias value. Resonances appear when the bias energy matches an integer number of modulation quanta. They constitute the atomic counterpart of Shapiro resonances observed in microwave-driven superconducting Josephson junctions. The population dynamics near each resonance corresponds to slow and non-linear secular oscillations on top of a rapid `micromotion'. At long times and in a narrow window of modulation frequencies around each resonance, we observe a relaxation to asymptotic states that are unstable without drive. These stationary states correspond to phase-locked solutions of the Josephson equations generalized to include dissipation, and are analogous to the stationary states of driven superconducting junctions. We find that dissipation is essential to understand this long-time behavior, and we propose a phenomenological model to explain quantitatively the experimental results. Finally, we demonstrate hysteresis in the asymptotic state of the driven spinor BEC when sweeping the modulation frequency across a Shapiro resonance

Estabilidad y ley de área para sistemas cuánticos disipativos con equilibración rápida

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Departamento de Análisis Matemático, leída el 07-07-2016Desde su origen, la teoría de la información ha tenido fuertes conexiones con la mecánica estadística: el mismo término entropía de la información fue elegido por Shannon a partir del término usado en termodinámica, bajo sugerencia de Von Neumann [5, 67, 82]. Tradicionalmente la teoría de la información estudia el almacenamiento (códigos) y la transmisión a través de canales con ruido (capacidad de comunicación). Al interpretar las interacciones físicas como canales de comunicación, ha sido posible aplicar las mismas técnicas e ideas para entender cómo un sistema mecánico compuesto de muchas (o infinitas) partes desarrolla un comportamiento colectivo a partir de las interacciones simples y limitadas entre sus componentes individuales. Esto ha permitido entender el mecanismo con el cual propiedades macroscópicas aparecen como efectos de interacciones microscópicas. La misma relación se ha desarrollado recientemente entre las correspondientes generalizaciones cuánticas de ambas teorías: la información cuántica (que estudia el almacenamiento y la manipulación de la información en sistemas cuánticos) y la física de muchos cuerpos. Las conexiones entre los dos campos aumentan cada día y van en las dos direcciones: herramientas e ideas de la información cuántica ayudan a solucionar problemas abiertos en teoría de la materia condensada, y nuevos modelos de muchos cuerpos se desarrollan para aplicaciones de la información cuántica. Almismo tiempo la implementación y el control experimental de pequeños sistemas cuánticos ha mejorado de forma espectacular, aumentando la posibilidad de que estos experimentos se puedan llevar a cabo a escala más grande. Experimentos más grandes significa estar cada vezmás cerca de aplicaciones prácticas, lo cual ha orientado hacia el campo el interés de importantes universidades y centros de investigación, así como agencias nacionales de financiación como el EPSRC y la NSF, empresas privadas con fuerte inversión en la investigación y el desarrollo como IBM, Microsoft y Google...Since its origins, the field of information theory has had strong ties to statistical mechanics: the terminology entropy of information was borrowed by Shannon from the thermodynamic entropy, as suggested by Von Neumann [5, 67, 82]. Traditionally information theory studies the storage of information (coding) and its transmission in noisy channels (communication capacity). By interpreting the physical interactions as communications channels, it has been possible to apply the same tools and ideas in order to understand how the collective behavior of a mechanical system composed of many (or infinite) parties emerges from the simple and limited interactions between its individual components. This has lead to understand the mechanism by which macroscopic properties emerge as effective behavior from microscopic interactions. The same relationship has been developed recently between the corresponding quantum generalizations of both theories: quantuminformation (which is interested in the storage and manipulation of information in quantummechanical systems) andmany-body quantumphysics. The ever-growing number of connections between the two fields goes in both directions, with tools and ideas fromquantuminformation helping to solve long-standing problems in condensed matter physics, and new many-body models being developed for the storage and the transformation of quantum information. At the same time the spectacular improvements we have seen in the implementation and experimental control of small quantumsystems is fueling the expectation that these experiments could be scaled up in size. Larger experiments means being closer to have practical applications, which has driven interest from top universities and research centers, national funding bodies such as EPSRC and NSF, to private companies with a strong focus on technological research as IBM, Microsoft and Google...Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasTRUEunpu

Phases and phase transitions in disordered quantum systems

These lecture notes give a pedagogical introduction to phase transitions in disordered quantum systems and to the exotic Griffiths phases induced in their vicinity. We first review some fundamental concepts in the physics of phase transitions. We then derive criteria governing under what conditions spatial disorder or randomness can change the properties of a phase transition. After introducing the strong-disorder renormalization group method, we discuss in detail some of the exotic phenomena arising at phase transitions in disordered quantum systems. These include infinite-randomness criticality, rare regions and quantum Griffiths singularities, as well as the smearing of phase transitions. We also present a number of experimental examples.Comment: Pedagogical introduction to strong disorder physics at quantum phase transitions. Based on lectures given at the XVII Training Course in the Physics of Strongly Correlated Systems in Vietri sul Mare, Italy in October 2012. Submitted to the proceedings of this school. 60 pages and 23 figures. Builds on material reviewed in arXiv:cond-mat/0602312 and arXiv:1005.270

Dissipative solitons in pattern-forming nonlinear optical systems : cavity solitons and feedback solitons

Many dissipative optical systems support patterns. Dissipative solitons are generally found where a pattern coexists with a stable unpatterned state. We consider such phenomena in driven optical cavities containing a nonlinear medium (cavity solitons) and rather similar phenomena (feedback solitons) where a driven nonlinear optical medium is in front of a single feedback mirror. The history, theory, experimental status, and potential application of such solitons is reviewed