Faculty of Physics University of Warsaw > Events > Seminars > Exact Results in Quantum Theory

Exact Results in Quantum Theory

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room 1.40, Pasteura 5 at 13:00

Marcin Krych (FUW)

Confluent equation

room 1.40, Pasteura 5 at 14:15

Pavlos Kassotakis (IFT UW)

3D-compatible maps and integrable difference systems

In this talk the notions of 3D-compatible, Yang-Baxter and Braid maps will be introduced, together with their interrelations andtheir connections to integrable difference systems. Furthermore,derivations and extensions of these maps to skew-fields will bediscussed. The latter will result to the extension and generalizationof integrable difference systems to totally non-commutating variables.In that respect we obtain the non-Abelian lattice-modifiedGel’fand-Dikii hierarchy,together with the explicit form of anon-Abelian hierarchy that we refer to as the lattice-NQC Gel’fand-Dikii hierarchy.

room 1.40, Pasteura 5 at 14:15

no seminar

room 0.03, Pasteura 5 at 12:15

Alexander Turbiner (ICN-UNAM, Mexico and Stony Brook University)

n-body problem: quantum and classical

Many body problem plays a central role in many physics sciences including celestial mechanics, atomic-molecular physics, nuclear physics. Its main characteristics is that the potential in both non-relativistic CM and QM de-pends on relative distances between bodies alone being translation-invariant.A new concept is proposed: to study particular solutions of n-body problem,both classical and quantum, which depend on relative distances ALONE. In such a case n-body problem becomes less dimensional and equivalent to ei-ther classical/quantum top in constant magnetic field or to multi-dimensional particle moving in curved space with some remarkable cometric. Since the ground state function — the main object in quantum mechanics — and choreography in classical mechanics are functions of relative distances ONLY they can be treated in much simpler way then up to now. Analogue of kineticenergy is (Lie)-algebraic operator which can be written in terms of sl(n(n+1)/2) algebra generators. Solvable but non-integrable 3-body harmonic oscillator might be briefly discussed.

room 1.40, Pasteura 5 at 14:15

Arman Taghavi-Chabert (IFT UW)

Introduction to CR geometry and applications, part II

In its simplest form, CR geometry can be understood as the study of real hypersurfaces in complex space. In this talk, I will present the basics of the topic and introduce the audience to the Webster-Tanaka calculus in the case where the CR structure is also contact. I will explain how it interacts with Lorentzian conformal geometry especially in connection with mathematical relativity.

room 1.40, Pasteura 5 at 14:15

Michael Duetsch (U. Goettingen)

Analytic regularization, addition of local counter terms and a forest formula

It is proved that the widespread method of treating UV-divergences in pert.QFT by regularization and renormalization (i.e., addition of local counter terms) can be used to construct a solution of the axioms of causal perturbation theory. First we obtain an inductive formula for the $S$-matrix, which we then solve by a "forest formula'' (corresponding to Zimmermann's forest formula for BPHZ renormalization). For scalar fields the resulting renormalization method is always applicable.

join us at 14:15

Muxin Han (Florida Atlantic University)

4-dimensional covariant Loop Quantum Gravity and complex Chern-Simons theory

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,C) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex.
Zoom link: https://uw-edu-pl.zoom.us/j/91655352625?pwd=Z0k4SU1DS3VpL05uQXZicnJ1S28zQT09

room 1.40, Pasteura 5 at 14:15

Arman Taghavi-Chabert (IFT UW)

Introduction to CR geometry and applications

room 1.40, Pasteura 5 at 14:15

no seminar

room 1.40, Pasteura 5 at 14:15

Jochen Zahn (Leipzig University)

Quantum fields near Cauchy horizons

The strong cosmic censorship hypothesis requires that the stress tensor diverges at a Cauchy horizon, in order to prevent the breakdown of determinism associated to the non-unique extension beyond it. However, it has recently been established that at the Cauchy horizon of near extremal Reissner-Nordström-deSitter (RNdS) black holes the divergence of classical field perturbations becomes weak enough to allow for a non-unique extension (as a weak solution) beyond the Cauchy horizon, indicating a violation of strong cosmic censorship. In contrast, for quantum fields on RNdS we find that the degree of divergence of the expectation value of the renormalized stress tensor near the Cauchy horizon is state-independent, universal, and strong enough to save strong cosmic censorship and to drastically change the nature of the singularity inside the black hole. Based on joint work with Stefan Hollands, Christiane Klein, Bob Wald.

room 1.40, Pasteura 5 at 14:15

no seminar

room 1.40, Pasteura 5 at 14:15

Krzysztof Jachymski (IFT UW)

Taming the complexity of hybrid quantum systems

Quantum many-body systems are characterized by exponentially large Hilbert space, which makes them difficult to model efficiently. Quantum simulators can act as a bridge between simplistic models and more complex ones. We show how to realize the extended Hubbard-Holstein model relevant for materials with strong electron-phonon coupling in an AMO setup using a mixture of Rydberg and ground state atoms. We discuss a variational numerical method designed to access the phase diagram of the system and its extension to other hybrid systems such as the Dicke model.

room 1.40, Pasteura 5 at 14:15

Jan Derezinski (IFT UW)

The Feynman propagator on a curved spacetime

Quantum Field Theory on curved spacetimes is one of the most basic formalisms of theoretical physics. It might be expected that one cannot say anything new about its foundations. Surprisingly, it seems that some elements of its basic mathematical structure have been clarified only recently in my work with Daniel Siemssen.One of such elements is the notion of the (in-out) Feynman propagator. I will explain what it is in asymptotically stationary stable spacetimes. I will also discuss how the Feynman propagator is related to the essential self-adjointness of the Klein-Gordon operator.

room 1.40, Pasteura 5 at 14:15

Krzysztof Myśliwy (IFT UW)

On the equation of state of fermions with all-to-all attractive interactions: from the classical hard-core lattice gas to ideal bosons

We consider a simple model of interacting fermions in low dimensions, with the long-range attractive force giving rise to an all-to-all interaction (Kac limit). We discuss the stability conditions for the thermodynamics to exist, and find the grand canonical partition function exactly. It turns out that upon varying the embedding dimension, or, equivalently, the exponent in the dispersion relation, the equilibrium thermodynamics of the system varies dramatically and is accompanied by a first-order phase transition at low dimensions, which vanishes at the boundary dimension for thermodynamics to exist, where it is replaced by complete and exact bosonization. If time permits, we shall discuss extensions to the case of a spin-polarized dilute Fermi gas with an additional short-range repulsion. Joint work with Marek Napiórkowski.

room 1.40, Pasteura 5 at 14:15

no seminar

no seminar

room 1.40, Pasteura 5 at 14:15

Robert Conte (Centre Borelli, École normale supérieure Paris-Saclay)

Bonnet surfaces and the natural Lax pair of the sixth Painlevé equation

The moving frame of the surfaces built by Bonnet in 1867 is extrapolated to a new, second-order, isomonodromic matrix Lax pair of the sixth Painlevé equation, whose elements depend rationally on the dependent variable and quadratically on the monodromy exponents $\theta_j$. Next, by converting back this Lax pair to a moving frame, we obtain an extrapolation of Bonnet surfaces to analytic surfaces with two more degrees of freedom.

room 1.40, Pasteura 5 at 14:15

Wojciech Kamiński (IFT UW)

Wald axioms and the quantum stress energy tensor

room 1.40, Pasteura 5 at 14:15

Andrzej Dragan (FT UW + National University of Singapore)

Superluminal relativity in 1+3 spacetime

We develop an extension of special relativity to account for superluminal inertial observers in 1+3 dimensional spacetime. It turns out that even for superluminal observers the speed of light is preserved and no obvious logical inconsistencies arise. The price to be paid is the unusual physics within superluminal frames as well as the fact that classical physics has to be abandoned and quantum field theory becomes a necessity within such frameworks. We also argue that superluminal particles may not only be a mathematical possibility, but they could actually exist within the known components of the Standard Model.

room 1.40, Pasteura 5 at 14:15

Pedram Karimi (IFT UW)

Superintegrability in Matrix Models

Multipoint correlation functions can be expanded as an average of different bases (characters) in the space of symmetric polynomials. It turns out that for many models there exists a basis where the average of character takes a simple factorized form , written in the term of character again. This character preservation property is called superintegrability. In this talk, I will review and outline the proof of superintegrability in the beta deformed eigenvalue models. This is based on a joint work with A. Bawane and P. Sułkowski.

room 1.40, Pasteura 5 at 14:15

Kasia Rejzner (University of York)

Interacting quantum fields in (perturbative) algebraic quantum field theory

In this talk I will present the framework of perturbative algebraic quantum field theory (pAQFT), developed over theyears by Brunetti, Duetsch, Fredenhagen, myself and many others. This approach allows one to mathematically describephysically relevant QFT models in Lorentzian signature (also on curved spacetimes). It combines the locality idea coming from algebraic quantum field theory (AQFT) with methods of perturbation theory, including homological algebra and formal deformation quantisation. Recently a non-perturbative version of the framework has been started by Buchholz and Fredenhagen and is currently under development by Brunetti, Duetsch, Fredenhagen and myself.

room 1.40, Pasteura 5 at 14:15

Paweł Jakubczyk (IFT UW)

The derivative expansion of the nonperturbative RG for the O(N) models

I will review the methodology of the nonperturbative renormalization group and present its application to study the critical behavior of the O(N) models.

room 1.40, Pasteura 5 at 14:15

Maciej Kolanowski (IFT UW)

Should physicists know about von Neumann algebras?

Probably not. On the off chance they should, I will introduce the concept and the basic classification with examples. Then, I will explain how quantum gravity could change the type of algebra, why that is a good thing and why the entropy in de Sitter spacetime is negative. Although the presented results (both in quantum theory and in gravity) are exact, the mathematical rigor shall be sacrificed to build a more convincing physical picture.Based mainly on 2206.10780 (Chandrasekaran, Longo, Penington and Witten, An Algebra of Observables for de Sitter Space)

room 1.40, Pasteura 5 at 14:15

Wojciech Kamiński (IFT UW)

Conformal version of Einstein's equations

The Fefferman-Graham obstruction tensor is an interesting conformal invariant, which vanishes on solutions of Einstein's equations. Although it is complicated and depends on high derivatives of the metric, it also shares many nice properties of the Einstein tensor. In particular, vanishing of the obstruction tensor has a well-posed initial value problem (it is hyperbolic in a suitable gauge). Due to conformal properties, this equation can serve as a useful tool for analyzing asymptotic behaviour of solutions of the Einstein field equations. The proof of hyperbolicity is not trivial and it involves ambient metric construction of Fefferman and Graham.

room 1.40, Pasteura 5 at 14:15

Igor Khavkine (Czech Academy of Sciences)

Triangular decoupling of harmonic gauge linearized gravity around a Schwarzschild black hole

I will review the motivations (from classical as well as quantum field theory) for studying electromagnetism and linearized gravity in harmonic gauge (locality and regularity, simplicity of residual gauge freedom, renormalization of interactions). Unfortunately, even after successful separation of variables, this choice of gauge leads to technical difficulties on non-flat backgrounds, like the Schwarzschild black hole, due to rather complicated radial mode equations. I will then describe a recent series of works, in which I have taken steps to overcome these difficulties by explicitly decoupling the radial mode equations into sparse triangular form. This simplification opens the door to immediate applications: solving the equations of motion with sources, proving the absence of exponentially growing modes, constructing Green functions, explicit formulas for Debye potentials, all directly in harmonic gauge.

room 1.40, Pasteura 5 at 14:15

Andreas Deuchert (Univeristy of Zurich)

The free energy of the two-dimensional dilute Bose gas

We prove a lower bound for the free energy of the two-dimensional dilute Bose gas in the thermodynamic limit. A matching upper bound has been obtained elsewhere. The resulting asymptotic formula for the free energy is interesting because the interaction term depends on the transition temperature of the Berezinskii–Kosterlitz–Thouless phase transition, which is conjectured to occur in the two-dimensional homogeneous Bose gas. This is joint work with Simon Maier and Robert Seiringer.

room 1.40, Pasteura 5 at 14:15

no seminar

room 1.40, Pasteura 5 at 14:15

Oleksandr Gamayun (IFT UW)

Exact results for one-dimensional mobile impurity

I will consider an integrable model of a mobile impurity propagating in a one-dimensional gas of free fermions. It is the simplest yet fundamental model capturing the peculiar physics and mathematics of the non-equilibrium processes. The integrability allows one to obtain a complete nonperturbative solution and express physical quantities in terms of the Fredholm determinants.
After a detailed analysis of these determinants, I will discuss several striking physical phenomena, such as incomplete relaxation and momentum-dependent impurity statistics. The universal properties of such one-dimensional systems can be described by the nonlinear Luttinger liquid (nLL). I will explain the microscopic derivation of nLL from the form factors and discuss the generalization to finite temperatures.

join us at 14:15

Min Lee (University of Oxford)

A Rigorous Computation of the Chiral Anomaly in Gauge Theories

The chiral anomaly in gauge theories in terms of the functional measure was first calculated by Fujikawa in the 1970s. The physical meaning of this anomaly is that the global chiral symmetry of classical gauge theories does not pass over to the local chiral symmetry of corresponding quantum theories. Mathematically, the chiral anomaly has topological implications because it demonstrates that the Dirac operator carries an index that depends solely on the configuration of the gauge fields. In this talk, I show how to formulate rigorously the standard calculations which yield the explicit form of the chiral anomaly.

Link: https://uw-edu-pl.zoom.us/j/97027158778?pwd=WHU4cDdDYjZKVDhVZGZFVllWcG04UT09
Meeting ID: 970 2715 8778
Passcode: 022707

room 1.40, Pasteura 5 at 14:15

Gustavo J. Turiaci (IAS, Princeton)

Black hole microstate counting from the gravitational path integral

Reproducing the integer count of black hole microstates from thegravitational path integral is an important problem in quantum gravity. In this talk I will show that, by using supersymmetric localization, the gravitational path integral for 1/8-BPS black holes in N=8 supergravity reproduces the index obtained in the string theory construction of such black holes, including all non-perturbatively suppressed geometries.