Projects / Programmes

# Thermodynamics of dissipative nanosystems

Code |
Science |
Field |
Subfield |

1.02.02 |
Natural sciences and mathematics |
Physics |
Theoretical physics |

Code |
Science |
Field |

P190 |
Natural sciences and mathematics |
Mathematical and general theoretical physics, classical mechanics, quantum mechanics, relativity, gravitation, statistical physics, thermodynamics |

Code |
Science |
Field |

1.03 |
Natural Sciences |
Physical sciences |

quantum mechanics, manybody systems, statistical physics, open systems, dissipation, transport

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Researchers (6)

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Organisations (2)

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Abstract

Summary
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Thermodynamics is the theory that describes behavior of macroscopic observables in systems that usually have many degrees of freedom. Quantum mechanics is on the other hand the theory of small systems with microscopic, in general non-commutative, observables, and tensor-product structure of the Hilbert space. The language and the scale at which they work best is seemingly different, although, in principle, one should be able to "derive" statistical laws that underlay thermodynamics purely from microscopic quantum mechanical laws.
Within classical systems there is a well established theory that tries to do that and is known as the theory of dynamical systems (or the ergodic or chaos theory). One of the important findings there is that already with a few-degree of freedom toy systems one can often capture generic chaotic behavior of a many-particle system. Because few-body systems are easier to analyze classical theory of dynamical systems is relatively mature and established field. However, microscopic dynamics is in principle quantum and in in quantum mechanics, due to a tensor-product structure, things are not that simple. Quantum systems can be qualitatively different than classical -- it is quantum information theory that exploits that -- and very importantly, complexity of a many-body quantum system grows exponentially with its size, rendering its analysis in general very difficult. As a consequence, quantum many-body physics is less explored, with many famous old problems outstanding (e.g., superconductivity, transport in the 1D Heisenberg model, etc.).
Several developments in recent years intensified our quest to understand many-body physics of quantum systems. On one hand there is experimental motivation: physics experiments are getting increasingly more advanced, being able to manipulate individual quantum systems. On the other hand there is also a technology-driven top-down impetus -- for instance, with increasingly miniaturized electronic components one has to understand interaction of nanoscopic systems with its environment, and in addition one would like to design devices that would exploit all the riches of quantum world. Not least, there is also purely theoretical and old motivation, to simply understand how and which statistical laws are obeyed by many-body quantum systems. Because such systems are usually exposed to the environment, either unavoidably or intentionally, one in fact has to deal with dissipative systems.
The aim of the proposed project is to study statistical properties of many-body dissipative systems. We would like to stress that most of the questions that we plan to study are rather unexplored for dissipative many-body systems. We deem several questions to be very important -- judged by their famous counterparts studied extensively in closed Hamiltonian systems. We are confident that such pioneering research is a guarantee for interesting new discoveries. In particular, we shall deal with spectral properties of dissipative propagators, like the famous spectral gap question. Being a non-hermitian linear operator this opens up a completely new field, as in closed systems one usually deal with hermitian operators. Another important topic that we plan to study is computational power with limited resources. An important example are limits on cooling techniques with given (realistic, e.g., local) couplings. We are also going to study emergent laws in many-body systems, like transport, rectification, or thermoelectric coefficients, as well as analyze fluctuations in simple quantum machines, with a particular stress on the validity or violations of thermodynamical laws. Finally, we are also going to search for new states and phases of matter as well as phenomena that can arise in many-body systems and out of equilibrium. One particularly appealing and hot topic is many-body localization.

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Significance for science

The topic of dissipative quantum systems has been around for many years, mostly in few-particle context, though in recent years many-body physics is coming to the forefront. Similar is the case with thermodynamics of quantum machines. We therefore strongly feel that the time is ripe for the two to be joined and implications studied. On one hand there are recent strong analytical results, on the other hand we also have strong numerical methods available. Thermodynamics as such is also of high inherent interest because it is not a microscopic theory and therefore it works regardless of the underlying microscopic theory. As such it has a special place in physics and understanding it at the level of another fundamental theory -- quantum mechanics -- is of rudimentary importance.
Our group has been leading top research in the past. Just as an example, despite being a relatively small project group having only 5 members, in the past 5 years we have published 23 papers in the premier journal Physical Review Letters.
Description of specific points follows.
Characterization of chaoticity and integrability in terms of spectral fluctuations for closed systems is one of the main achievements of quantum chaos theory. Doing a similar thing for dissipative systems under point 1.i) would be a major achievement. The gap problem under 1.ii) and its importance has been already stressed under point 11. Understanding relaxation rates in open systems is a step towards building up a coherent theory of nonequilibrium quantum system, something that is at present already rather understood in the classical domain.
Controllability studied in 2.i) and the likes of cooling techniques are not just of theoretical importance, but even more of experimental value. Here we stress again that the Lindblad setting that we plan to study is a natural setting used in quantum optics and can correctly account for modern cold-matter experiments. Considering that this is one of the more propulsive fields of physics the impact is guaranteed.
Transport studies of model systems in 3.i) are important for theoretical understanding of emergent phenomena. We note that some of the most celebrated problems in physics, like high-Tc superconductivity, are believed to be explainable by theoretical models in question. Also, finally resolving the nature of transport in the Heisenberg model would solve a very old problem. Topic with perhaps most immediate applied importance is thermoelectricity. Any breakthrough in this area would have implications beyond science.
Many-body localized phase studied in 4.i) is an important subject because it is a phase with properties like no other known state of matter. This explains an almost explosive interest in recent two years (more than 90 papers on the subject have been submitted to the arXiv in 2014 alone). We have already demonstrated leadership in the field (our 2008 PRB paper was among the first studies).

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Significance for the country

The project will contribute to the development of basic science. Nevertheless some of the points are closer to applied science and can have more immediate applications. Notable such cases are points 2.i) -- controllability, and 2.ii) nanomachines, as well as point 3.i) transport studies with thermoelectricity.
Other questions studied are at present more of a theoretical nature, however, they will contribute to understanding the three more applied points.
Controllability and quantum cooling as well as quantum nanodevices and their efficiency might at present be in the domain of laboratories, however progress in these fields is so rapid that this could change on a scale of next 5-10 years. To give an example, quantum cryptography was just a theoretical concept 10 years ago -- today there are few commercial companies that sell commercial quantum cryptography devices (customers are big banks, government organizations, military, etc..). While we certainly will not have useful quantum computers within next 10 years, some other quantum devices are possible. This particularly holds for semiconductor-based devices and/or photon-based devices. Thermodynamics at a nanoscale is also of wider interest for electronics industry.
Topic with most implications for wider society though is the study of transport and in particular of thermoelectricity. Thermoelectricity, or the quest for high ZT, is a huge field spanning several field of science: it is of interest in materials science, chemistry, physics, and theoretical physics. Today, with best ZT of around 2 we are already quite close to the breaking point of ZT=3, beyond which thermoelectric devices could be widely commercially viable. This would bring with it many applications that would probably completely change the way we deal with energy. One could for instance improve efficiencies by harnessing waste heat (for instance, all larger car companies have rather secretive projects going on to recuperate exhaust waste heat, increasing fuel efficiency by upto 10%. Currently they are supposedly able to recuperate about 500 W of power).
Results in the field of transport and thermoelectricity would also contribute towards modern goals of society -- responsible use of energy and greener environment.

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Most important scientific results

Interim report,
final report
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Most important socioeconomically and culturally relevant results

Interim report,
final report