Open Quantum Dynamics with Nonlinearly Realized Symmetries.
Jury Radkovski Perimeter Institute for Theoretical Physics
1417 - 1428 of 20118 Results
Format results
Lecture - Relativity, PHYS 604
Ghazal Geshnizjani Perimeter Institute for Theoretical Physics
Lecture - Beautiful Papers
Pedro Vieira Perimeter Institute for Theoretical Physics
Lecture - QFT II, PHYS 603
Francois David CEA Saclay
Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
Uma DivakaranICTS:30360Late-time signals from binary black hole mergers
Marina de AmicisThe Gaudin model in the Deligne category Rep $GL_t$
Leonid Rybnikov
Open Quantum Dynamics with Nonlinearly Realized Symmetries.
Jury Radkovski Perimeter Institute for Theoretical Physics
In the framework of Non-Equilibrium Field Theory, I will construct the effective influence functional — generator of non-equilibrium correlation functions — for a mechanical system with degrees of freedom living on a group (e.g. rigid body) interacting with a thermal bath at high temperature. I will derive the constraints on the influence functional following from the group symmetry structure and the DKMS symmetry — generalization of the fluctuation-dissipation theorem. At the linear response level, group symmetry turns out to impose more constraints compared to DKMS. I will illustrate the general formalism with the diffusion in a Fermi gas and exhibit the large-N suppression of the non-linear response. Finally, I will introduce the Universal Bath — the generalization of the Caldeira-Leggett model. It is a dual field theory defined in one extra dimension that reproduces the classical non-equilibrium dynamics of the mechanical system. I will show that in the limit of Ohmic dissipation, when the temperature becomes the only relevant scale at play, the Universal Bath also reproduces the quantum corrections.
Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling
Kirill NeklyudovThe 3rd talk of a monthly webinar series jointly hosted by Perimeter, IVADO, and Institut Courtois.Rare event sampling in dynamical systems is a fundamental problem arising in the natural sciences, which poses significant computational challenges due to an exponentially large space of trajectories. For settings where the dynamical system of interest follows a Brownian motion with known drift, the question of conditioning the process to reach a given endpoint or desired rare event is definitively answered by Doob's h-transform. However, the naive estimation of this transform is infeasible, as it requires simulating sufficiently many forward trajectories to estimate rare event probabilities. In this talk, I'll present our recent findings on the variational formulation of Doob's h-transform as an optimization problem over trajectories between a given initial point and the desired ending point. To solve this optimization, we propose a simulation-free training objective with a model parameterization that imposes the desired boundary conditions by design. Our approach significantly reduces the search space over trajectories and avoids expensive trajectory simulation and inefficient importance sampling estimators which are required in existing methods. We demonstrate the ability of our method to find feasible transition paths on real-world molecular simulation and protein folding tasks.
Lecture - Beautiful Papers
Pedro Vieira Perimeter Institute for Theoretical Physics
Lecture - QFT II, PHYS 603
Francois David CEA Saclay
Topological Superconductivity hosting Majorana States in Magnet/Superconductor Heterostructures
Arijit SahaICTS:30361Our theoretical investigation explores a feasible route to engineer the two-dimensional (2D) Kitaev model of first-order topological superconductivity (TSC) introducing a magnetic spin texture. The main outcome of 2D Kitaev’s model is that a px + py type superconductor can exhibit a gapless topological superconducting phase in bulk hosting non-dispersive Majorana flat edge mode (MFEM) at the boundary. Our proposed general minimal model Hamiltonian is suitable to describe magnet/superconductor heterostructures. It reveals robust MFEM within the emergent gap of Shiba bands, spatially localised at the edges of a 2D magnetic domain of spin- spiral. We finally verify this concept from real material perspectives by considering Mn (Cr) monolayer grown on an s-wave superconducting substrate, Nb(110) under strain (Nb(001)). In both the 2D cases, the antiferromagnetic spin-spiral solutions exhibit robust MFEM at certain domain edges. This approach, particularly when the MFEM appears in the TSC phase for such heterostructure materials, offers significant prospect to extend the realm of TSC in 2D. Very recently, we expand this theoretical framework for engineering a 2D second-order topological superconductor (SOTSC) by utilizing a heterostructure: incorporating noncollinear magnetic textures between an s-wave superconductor and a 2D quantum spin Hall insulator. It stabilizes the SOTSC phase within the Shiba band, resulting in Majorana corner modes (MCMs) at the four corners of a 2D domain. The calculated non-zero quadrupole moment characterizes the bulk higher-order topology. Analytically calculated effective pairings in the bulk illuminate the microscopic behaviour of the SOTSC. Such first and second order Majorana modes are believed to be the building blocks for the fault-tolerant topological quantum computation.
Reference: Phys. Rev. B (Letter) 109, L041409 (2024) .
Phys. Rev. B (Letter) 109, L121301 (2024).Chaos controlled and disorder driven phase transitions induced by breaking permutation symmetry
Uma DivakaranICTS:30360The effects of disorder and chaos on quantum many-body systems can be superficially similar, yet their interplay has not been sufficiently explored. We study this using an all to all interacting spin chain with disordered interacting term in presence of periodic kicks. The disorder free version of this model shows regular and chaotic dynamics within permutation symmetric subspace as the interaction strength is increased. When the disorder is increased, we find a transition from a dynamics within permutation symmetric subspace to full Hilbert space where the expectation values of various operators are given by random matrix theory in full Hilbert space. Interestingly, finite size scaling predicts a continuous phase transition at a critical disorder strength.
Towards realistic tensor network holography using loop gravity
Simon LangenscheidtPIRSA:24110084In order to understand many Quantum information aspects of the Ads/CFT correspondence, tensor network toy models of holography have been a useful and concrete tool. However, these models traditionally lack many features of their continuum counterparts, limiting their applicability in arguments about gravity. In this talk, I present a natural extension of the tensor network holography paradigm which rectifies some of these issues. Its direct inspiration originates in Loop Quantum Gravity, which allows not only lifting existing limitations of tensor networks, but also firmly grounds the models in the context of nonperturbative canonical quantum gravity.
Late-time signals from binary black hole mergers
Marina de AmicisLate-time tails emitted by binary black holes mergers contain invaluable information on the spacetime’s asymptotic structure. Perturbative numerical simulations of extreme mass-ratio mergers have revealed that these tails are enhanced by several orders of magnitude with the progenitors’ binary eccentricity. This amplification has the potential to bring tails within the realm of observation and shows that this effect carries significant astrophysical implications, other than fundamental physics content.I will present an analytical perturbative model that accurately predicts the numerically observed tail and explains its enhancement with the progenitors' binary eccentricity. The model is an integral over the system's entire history, showing how the post-ringdown tail is inherited from the non-circular inspiral in a non-local fashion. I will prove the tail to be a superposition of many power-laws, with each term's excitation coefficient depending on the specific inspiral history. A single power law is recovered only in the limit of asymptotically late times, consistent with Price's results and the classical soft-graviton theorem. Finally, I will introduce a robust framework for extracting tails in fully non-linear simulations of equal masses mergers. I will present results for late-time tails emitted by these systems and discuss their phenomenology.The Gaudin model in the Deligne category Rep $GL_t$
Leonid RybnikovDeligne's category $D_t$ is a formal way to define the category of finite-dimensional representations of the group $GL_n$ with $n=t$ being a formal parameter (which can be specialized to any complex number). I will show how to interpolate the construction of the higher Hamiltonians of the Gaudin quantum spin chain associated with the Lie algebra $\mathfrak{gl}_n$ to any complex $n$, using $D_t$. Next, according to Feigin and Frenkel, Bethe ansatz equations in the Gaudin model are equivalent to no-monodromy conditions on a certain space of differential operators of order $n$ on the projective line. We also obtain interpolations of these no-monodromy conditions to any complex $n$ and prove that they generate the relations in the algebra of higher Gaudin Hamiltonians for generic complex $n$. I will also explain how it is related to the Bethe ansatz for the Gaudin model associated with the Lie superalgebra $\mathfrak{gl}_{m|n}$.This is joint work with Boris Feigin and Filipp Uvarov,https://arxiv.org/abs/2304.04501.