Non-Equilibrium Dynamics in Closed Interacting Quantum Systems

Nontechnical summary

This award supports theoretical and computational research and education into quantum mechanical systems of interacting particles far from equilibrium. The importance of quantum physics in technology is rapidly growing. Quantum mechanics combines both particle and wave concepts leading to unintuitive but very robust effects used in modern technology.

In recent years, the focus of quantum research has shifted to non-equilibrium phenomena including but not limited to quantum computation and simulation in complex circuits, various high-precision metrological applications, and designing quantum materials with desired properties by driving them away from thermal equilibrium.

This project focuses on two major themes: i) understanding, characterizing and controlling chaos in interacting many-particle systems and ii) developing formalism for describing systems which have both quantum and classical degrees of freedom interacting with each other.

Most systems around us are chaotic. On the one hand chaos reduces our ability to predict and control the behavior of various systems. On the other, it leads to long time stability of matter.

Colloquially, the situation is like with tornadoes: they appear because of chaos leading to instabilities in the atmosphere and they disappear also because of chaos eventually relaxing to a homogeneous state dictated by the laws of equilibrium statistical mechanics, which would not exist without chaos. The P.I. and his group recently developed a new framework of defining and characterizing both quantum and classical chaotic systems using a geometric approach.

In the current project, the P.I. will focus on universal (model independent) aspects of chaos focusing on least studied intermediate and long-time behavior of such systems. A special focus will be on finding similarities and differences between quantum and classical chaotic systems.

The second thrust is focused on the interplay between fast quantum and slow classical degrees of freedom. A colloquial example is a bucket with water. When classical bucket quickly rotates, the quantum water molecules form a new equilibrium state where water stays in the bucket even when it is upside down.

This happens because quantum and classical degrees of freedom cannot be easily separated from each other forming a joint synchronized motion. While this example with rotations is of course well understood, for more complex motions like crystal vibrations, the existing theoretical framework, known as the Born-Oppenheimer approximation (BOA), is insufficient.

The PI and collaborators have just developed a new general approach allowing one to systematically go beyond the BOA and describe such systems. In the current project PI plans to apply this approach to specific setups relevant to materials and other experimental platforms.

The main broader impact is a commitment to finish a new graduate level textbook on quantum mechanics with the expected completion date in mid-2026. The book (co-authored with M. Rigol and P.

Claeys) gives a new perspective on quantum physics shifting focus from understanding atomic orbitals to concepts relevant for understanding modern technology. The PI, also actively continues training students at all levels and performing extra curriculum teaching at various US and international short-term schools.

Technical summary

This award supports theoretical and computational research and education into quantum mechanical systems of interacting particles far from equilibrium. The research part of this proposal has two main themes: i) understanding quantum and classical chaos and ergodicity through adiabatic transformations and ii) systematic expansion of dynamics of systems with joint classical and quantum degrees of freedom beyond Born-Oppenheimer approximation (BOA).

As it was shown by PI and collaborators adiabatic transformations connect into a single framework many seemingly different phenomena like emergence of local conservation laws, Schrieffer-Wolff transformations, Floquet Hamiltonians, short and long-time dynamics and operator growth, quantum chaos and ergodicity, design of fast and efficient quantum annealing protocols and quantum thermal machines. There also emerged new ideas, which will be central to this proposal like connecting quantum and classical chaos/ergodicity into a single framework, universal dynamics of systems close to integrability, and a systematic approach allowing one to go beyond the BOA for describing systems with quantum and classical degrees of freedom like molecules or electron-phonon systems.

Using this approach PI also plans to study emergent nonequilibrium steady states as states approximately equilibrating in the moving frame and, in particular, to understand how these non-perturbative states affect macroscopic physical observables like transport coefficients. PI will continue close interactions with experimental groups to test these theoretical ideas in various setups such as cold atoms, trapped ions, NV-centers, superconducting qubits, and various other quantum simulators.

The main broader impact is a commitment to finish a new graduate level textbook on quantum mechanics with the expected completion date in mid-2026. The book (co-authored with M. Rigol and P.

Claeys) gives a new perspective on quantum physics, shifting focus from understanding atomic orbitals to concepts relevant for understanding modern technology. The PI also actively continues training students at all levels and performing extra curriculum teaching at various US and international short-term schools.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.