PhD Projects

PhD projects: Interested students must email me a small motivation letter (max 1 page). I do not need a fancy copied/artificial letter. Simply explain the motivation behind opting for PhD, your research interests; these need not match with the areas or project mentioned below.

You are also welcome to discuss projects and topics other than those listed below.

Project 1: VS01

Title: Out-of-equilibrium quantum many-body dynamics
Broad area(s): Statistical Physics; Condensed Matter Physics; HEP
Keywords: Many-body localization; Integrability; Quantum thermalization; Quantum information
Theory/Experiment/Mixed: Theoretical and computational
Supervision: Single
Background required: Strong background in core theoretical subjects, especially quantum mechanics, mathematical physics, statistical physics and condensed matter physics. A good exposure to subjects in high energy physics (quantum field theory) would be very useful, but not essential. The candidate must have a very good computer programming skill.


Project description: Study of quantum matter pushed out of equilibrium offers a very interesting opportunity to investigate some fundamental questions that now lie at the interface of quantum statistical physics, condensed matter physics, high energy physics and quantum information. One of the central questions is: How do closed complex many-body quantum systems driven out of equilibrium thermalize? The dynamics ensuing post quench, ramps or following periodic driving evolves ultimately towards a state of a thermal equilibrium in most generic quantum systems. As the system evolves, quantum information present in the initial state gets scrambled because of the entanglement of local degrees of freedom. However, it may happen that the system fails to thermalize because of the phenomena of many-body localization. Note that the experimental realization of versatile precisely controlled and tunable quantum simulators (e.g., ultracold atoms in optical lattices) and quantum computers provides a fertile playground to test theoretical ideas. Similarly, strong cooling quench experiments in ultra-cold one-dimensional Bose gas have revealed a universal scaling dynamics far from equilibrium during the relaxation, associated with the approach of a non-thermal fixed point. In this thesis, we propose to examine the above complex non-equilibrium dynamical evolution for model systems in condensed matter physics.


References:

  1. J Eisert, M Friesdorf and C. Gogolin. Quantum many-body systems out of equilibrium. Nature Physics, 11, 124-130, 2015.
  2. J Kurchan. Quantum Bound to Chaos and the Semiclassical Limit. J Stat Phys 171:965-979 (2018).
  3. K Hashimoto, K Murata and R Yoshii. Out-of-time-order correlators in quantum mechanics. JHEP 10, 138, 2017.
  4. F Alet and N Laflorencie. Many-body localization: An introduction and selected topics. C R Physique 19, 498-525, 2018.
  5. S Erne et al. Universal dynamics in an isolated one-dimensional Bose gas far from equilibrium. Nature 563 (7730), 225-229, 2018.
  6. Y Liao and V Galitski. Emergence of many-body quantum chaos via spontaneous breaking of unitarity. Phys. Rev. B 105, L140202, 2022.
  7. M Ippoliti, T Rakovszky and V Khemani. Fractal, Logarthimic, and Volume-Law Entangled Nonthermal Steady States via Spacetime Duality. Phys. Rev. X 12, 011045, 2022.
  8. O A Castro-Alvaredo, B Doyon and T Yoshimura. Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium. Phys. Rev. X 6, 041065, 2016

Project 2: VS02

Title: Quantum algorithms for simulating classical and quantum fluids
Broad areas: HEP; Statistical Physics; Complex Systems; Nonlinear Physics
Keywords: Quantum computing; Quantum information; Statistical Physics; High Performance Computing
Theory/Experiment/Mixed: Theoretical and computational
Supervision: Single
Background required: Strong background in core theoretical subjects, especially quantum mechanics, mathematical physics, and statistical physics. Exposure to theoretical computer science would be useful, but not essential. The candidate must have a very good computer programming skill.


Project description: Slowly we are inching towards a new revolution in computational sciences. Stable and powerful quantum computers may become a reality in the years to come. Dedicated quantum algorithms are designed to speed up the solution of a given computational problem on quantum computers. In general, the aim is to go beyond the capabilities of a classical computer. This thesis proposal aims to both develop new and use existing quantum algorithms in order to simulate classical and quantum fluids and a few select model quantum systems in condensed matter physics. A related problem would involve designing algorithms to circumvent the problems that are encountered while carrying out a largescale simulation of classical and quantum fluids on classical supercomputers.


References:

  1. Montanaro, A. Quantum algorithms: an overview. npj Quantum Inf 2, 15023 (2016). https://doi.org/10.1038/npjqi.2015.23
  2. A W Harrow and A Montanaro. Quantum computational supremacy. Nature, Reviews Vol 549, page 203. https://doi:10.1038/nature23458
  3. Gaitan, F. Finding flows of a Navier–Stokes fluid through quantum computing. npj Quantum Inf 6, 61 (2020). https://doi.org/10.1038/s41534-020-00291-0
  4. Oz, F., Vuppala, R.K.S.S., Kara, K. et al. Solving Burgers’ equation with quantum computing. Quantum Inf Process 21, 30 (2022). https://doi.org/10.1007/s11128-021-03391-8
  5. Barratt, F., Dborin, J., Bal, M. et al. Parallel quantum simulation of large systems on small NISQ computers. npj Quantum Inf 7, 79 (2021). https://doi.org/10.1038/s41534-021-00420-3
  6. N. Ray et al. Towards Solving the Navier-Stokes Equation on Quantum Computers. arXiv:1904.09033. https://doi.org/10.48550/arXiv.1904.09033

Project 3: VS03

Title: Turbulence and nonequilibrium states in quantum fluids: Applications to astrophysical systems
Broad area: Statistical physics; Astrophysics; Condensed Matter Physics
Keywords: Turbulence; Nonlinear physics; Quantum Fluids; Fluid dynamics; Neutron stars; Dark Matter; Compact object formation; High Performance Computing
Theory/Experiment/Mixed: Theoretical and computational
Supervision: Single
Collaborator: Sergey Nazarenko
Skills: Strong background in core theoretical subjects, especially quantum mechanics, mathematical physics, statistical physics and condensed matter physics. The candidate must have a very good computer programming skill. Exposure to elementary astrophysics/cosmology/astrophysical fluid dynamics would be useful, but not essential.


Project description
Turbulence, a ubiquitous phenomenon in classical fluids, also occurs in quantum fluids, such as superfluid helium-4, 3He-B, Bose- Einstein condensates in traps, etc. A strongly turbulent state of a three-dimensional (3D) superfluid involves an interacting, dynamic tangle of quantized vortices on top of a condensate in the presence of random waves and other coherent structures. Moreover, nonlinearly interacting random waves give rise to an out-of-equilibrium system, called wave turbulence, characterized by the presence of inter-length-scale transfers (cascades) of certain quantities, e.g., an inverse cascade of particles towards large length scales, which describes the non-equilibrium Bose- Einstein condensation process.
The proposed thesis will examine the universal behavior of these nonlinear and nonequilibrium features for a variety of condensed matter and astrophysical systems and come up with simple minimal models.


Context: Bose-Einstein condensation (BEC), a macroscopic quantum phenomenon, is now routinely realized in laboratory experiments in systems involving ultracold atoms, polaritons-excitons, photons, magnons, etc. BECs are suggested to play an important role in the physics of astrophysical objects, such as neutron stars and provide interesting analogies in cosmology.
Paths leading to a BEC need not be in equilibrium, it is well known that ultracold Bose gases under cooling quenches pass through highly nonequilibrium states and may eventually lead to the formation of a condensate. This nonequilibrium relaxation dynamics of the quantum Bose gases and other quantum many-body systems has attracted a major attention, still the full understanding and characterization of the ensuing dynamics is far from complete. It has been argued that the dynamical evolution depends on the strength and nature of the cooling quench in closed systems leading to either wave turbulence-dominated states or nonthermal fixed points with universal scaling laws.
A general framework to study the nonlinear nonequilibrium (multi-scale) dynamical behavior of either quenched or forced -dissipated systems of weakly interacting ultracold Bose gases is the Gross-Pitaevskii theory. The aim of this proposal is to study above outlined behavior in a variety of systems of current interest to examine the emergent universal behavior in both strong turbulence and weak wave turbulence regimes.


Method: The thesis work will be primarily theoretical and computational. It will be at the interface of nonlinear physics, statistical physics, condensed matter physics and computational physics. Moreover, it will involve application of the fundamental ideas derived from the study of various turbulence and non-equilibrium states in quantum fluids to experimental condensed matter and astrophysical systems. The primary theoretical would be the hydrodynamic theory of superfluid Bose gases under driven-dissipated conditions; non-equilibrium statistical physics, wave turbulence and an understanding of strong hydrodynamic turbulence. Thus, the general framework would be the mean-field treatment of superfluid hydrodynamics, Gross-Pitaevskii theory and its variants.


Expected results: The proposed thesis will lead to a better understanding of the statistical properties of different types of turbulence and non-equilibrium states in quantum fluids. Large scale, as well as moderate but controlled, simulations of the GPE described superfluids would allow us to develop reduced models for the phenomenon occurring at small length scales. A comprehensive study of the wave turbulence regime would allow us to examine the extent of validity of the weak wave turbulence theory and predictions, and in particular would allow us to develop needed mathematical formulation study the interaction of waves with coherent structures.


References

  1. V Shukla and S. Nazarenko. Non-equilibrium Bose-Einstein Condensation. Phys. Rev. A 105 (3), 033305, 2022.
  2. A Griffin, V Shukla, M-E. Brachet, S. Nazarenko. Magnus-force model for active particles trapped on superfluid vortices. Phys. Rev. A 101, 053601 (2020).
  3. Skipp, V L’vov, S Nazarenko. Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics. Phys. Rev. A 102(4), 043318. 2020.
  4. J. A. P. Glidden, C. Eigen, L. H. Dogra, T. A. Hilker, R. P. Smith, and Z. Hadzibabic, Nat. Phys. 17, 457 (2021).
  5. B. Nowak, J. Schole, D. Sexty, and T. Gasenzer, Phys. Rev. A 85, 043627 (2012).
  6. V. Shukla, P. D. Mininni, G. Krstulovic, P. Clark di Leoni, M. Brachet. Quantitative estimation of effective viscosity in quantum turbulence. Physical Review A 99 (4), 043605, 2019.