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

Exact Results in Quantum Theory

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join us at 14:15

Tomasz Maciążek (University of Bristol)

Non-abelian quantum statistics on 1D wire networks

World lines of particles that exchange in 2D form braids in spacetime. These braids are subject to certain universal topological relations coming from their continuous deformations. In 2D, such an approach leads to the well-known braiding relation also known as the Yang-Baxter relation. In my talk, I will show how to define counterparts of braids and derive braiding relations for particles constrained to move on planar wire networks. In particular, I will demonstrate that particles on wire networks have fundamentally different braiding properties than particles in 2D. My analysis reveals an unexpectedly wide variety of possible non-abelian braiding behaviours on networks. The character of braiding depends on the topological invariant called the connectedness of the network. As one of our most striking consequences, particles on modular networks can change their statistical properties when moving between different modules. However, sufficiently highly connected networks already reproduce braiding properties of 2D systems.In the second part of my talk, I will analyse the ways of realising the braiding of anyons on networks in a topological quantum field theory setting where anyons are allowed to braid as well as fuse. The compatibility of fusion and braiding on networks leads to new types of hexagon equations which in turn allow more general braid actions than the ones which are known from 2D physics. [1] BH An, T Maciazek, Geometric presentations of braid groups for particles on a graph, Comm. Math. Phys. 384 (2) (2021)[2] T Maciazek, BH An, Universal properties of anyon braiding on one-dimensional wire networks, Physical Review B 102 (20), 201407 (2020)[3] A Conlon, J K Slingerland, Compatibility of Braiding and Fusion on Wire Networks, arXiv:2202.08207 (2022)

Link: https://us02web.zoom.us/j/84029651999?pwd=7tmWZrP9H5XKSwgebUoTESarH5tnjj.1 Meeting ID: 840 2965 1999 Passcode: 995804

room 1.40, Pasteura 5 at 14:15

Maciej Kolanowski (IFT UW)

A pancaked IR: novel fixed points for four-dimensional holographic theories

We show that almost all extremal black holes in Einstein-Maxwell-AdS theory develop diverging tidal forces at the horizon. This singularity in five (and higher) dimensions implies that the near horizon geometry of extreme Reissner-Nordstrom-AdS black holes are RG unstable under small changes of the boundary conditions at infinity. We found an infinite number of new one-parameter families of static extremal horizons. Their cross-sections are highly deformed three-spheres with an $SO(3)$ symmetry group. Numerical simulations show that generic boundary conditions at infinity lead to horizons belonging to a particular one-parameter family. Thus, this particular family is dual to new IR fixed points for the dual gauge theory. These fixed points seem to be stable under the RG flow, in contrast with the usual spherically symmetric ones. Joint work with Gary Horowitz and Jorge Santos.

room 1.40, Pasteura 5 at 14:15

Zoran Ristivojevic (Laboratory for theoretical physics, CNRS, Toulouse, France)

Several new exact results for the Lieb-Liniger model

The Lieb-Liniger model describes bosonic particles in one dimension that interact via a delta-function interaction. This model belongs to a small group of integrable models. It was exactly solved by Lieb and Liniger in 1963 using the Bethe ansatz. Despite that, extracting explicit analytical results for the quantities of interest is a formidable task. In this talk, we will overview several new exact results for the Lieb-Liniger model. The first is the perturbative expansion for the ground-state energy, which is obtained using the techniques of experimental mathematics. The second is the result for the boundary energy of the system, which was only approximatively solved by Gaudin in 1971. The third is the low-energy spectrum of elementary excitations. Finally, we will derive and discuss the difference-differential equation for the expectation values of the conserved charges of the model in the ground state, enabling one to obtain explicit analytical results.
[1] Z. Ristivojevic, Excitation Spectrum of the Lieb-Liniger Model, Phys. Rev. Lett. 113, 015301 (2014).
[2] A. Petković and Z. Ristivojevic, Spectrum of Elementary Excitations in Galilean-Invariant Integrable Models, Phys. Rev. Lett. 120, 165302 (2018).
[3] B. Reichert, G. E. Astrakharchik, A. Petković, and Z. Ristivojevic, Exact Results for the Boundary Energy of One-Dimensional Bosons, Phys. Rev. Lett. 123, 250602 (2019).
[4] Z. Ristivojevic, Conjectures about the Ground-State Energy of the Lieb-Liniger Model at Weak Repulsion, Phys. Rev. B 100, 081110(R) (2019).
[5] Z. Ristivojevic, Exact results for the moments of the rapidity distribution in Galilean-invariant integrable models, preprint, arxiv (2022).

room 1.40, Pasteura 5 at 14:15

Tomasz Cieślak (IMPAN)

Prandtl spirals as solutions to the 2d Euler

Prandtl spirals were introduced by L.Prandtl in 1922 as a model of vortices detaching from the edge of a wing. Still, their exact status was not clear till last year. In my talk I will speak about recent common result with P.Kokocki and W.S.Ozanski stating that Prandtl's spirals are weak solutions of 2d Euler.

room 1.40, Pasteura 5 at 14:15

Jacek Pawełczyk (IFT UW)

Three derivations of critical dimension in string theory

I shall discuss various approaches to quantization of the free bosonic string theory. I shall also show that the critical dimension D=26 arises due to the cancellation of various anomalies (Lorentz, conformal, Weyl) depending on the quantization scheme.

join us at 14:15

Xiaoxu Wu (Rutgers University)

Large time asymptotics of Schrödinger type equations with general data

We consider a Schrödinger equation with a general interaction term, which is linear or nonlinear, time-dependent and including charge transfer potentials. Without the assumption of radial symmetry, we prove the global solutions are asymptotically given by a free wave and a weakly localized part. The proof is based on constructing in a new way the Free Channel Wave Operator, and further tools from the recent work of Baoping Liu and Avy Soffer. Our work generalizes the results of the first part of their work to arbitrary dimension, and non-radial data. This is joint work with Avy Soffer.

Link (zoom):
https://us02web.zoom.us/j/84625427874?pwd=TzRHYnhmcTcvRk9kNWZPNTZzOUdDUT09
Meeting ID: 846 2542 7874
Passcode: 076159

join us at 14:15

Paolo Meda (Universita di Genova)

Semiclassical Gravity in Cosmology and Black Hole Physics

Semiclassical Gravity and Quantum Field Theory in Curved Spacetimes describe the propagation of a quantum matter field over classical curved spacetimes. Solutions of the so-called semiclassical Einstein equations, which govern the interplay between matter and geometry in the semiclassical regime, incorporate the backreaction of the quantum field on the background geometry. In this talk, I present some applications of the semiclassical Einstein equations in the framework of Cosmology and Black Hole Physics. In the former case, the proof of existence and uniqueness of local cosmological solutions is reviewed for a free massive scalar field arbitrary coupled with the curvature. In the latter case, the evaporation of spherically symmetric dynamical black holes sourced by the quantum trace anomaly is shown for a free massless, conformally coupled scalar field. Finally, the linear stability of semiclassical theories of gravity with higher-order derivative terms is discussed in a toy model, which mimics the evolution induced by semiclassical Einstein equations in physically relevant backgrounds, such as cosmological spacetimes.

Link: https://us02web.zoom.us/j/87158764274?pwd=QTdydXd3K1N4Vnpoc094N1o4ZTVNZz09(Meeting ID: 871 5876 4274 Passcode: 438484)

join us at 16:00

Elek Csobo (University of Innsbruck)

On blowup for the energy supercritical quadratic wave equation

We study the singularity formation for the focusing quadratic wave equation in the energy supercritical case, i.e., for d ≥ 7. We establish the existence of a new, non-trivial, self-similar blow-up solution u∗ in explicit form. For d = 9, we investigate the stability of u∗ without any symmetry assumptions on the initial data and show that there is a family of perturbations that leads to blow-up via u∗. In similarity coordinates, this family corresponds to a co-dimension one Lipschitz manifold modulo translation symmetries. This is a joint work with Birgit Sch ̈orkhuber and Irfan Glogic.

Link: https://us02web.zoom.us/j/87158764274?pwd=QTdydXd3K1N4Vnpoc094N1o4ZTVNZz09(Meeting ID: 871 5876 4274 Passcode: 438484)

join us at 14:00

Alexander Efremov ( )

Renormalization of SU(2) Yang-Mills theory with the flow equations

The goal of this work is a rigorous perturbative construction of the SU(2) Yang-Mills theory in four dimensional Euclidean space. The functional integration technique gives a mathematical basis for establishing the renormalization group equations. While introduction of a momentum space regulator removes the divergences of the Schwinger functions, the important difficulty of the approach is the fact that the regulator breaks the gauge invariance. Thus the main part of the work is to prove at all loop orders the existence of the vertex functions and the restoration of the Slavnov-Taylor identities in the limit of the vanishing regulator.

Link will appear shortly before the seminar

room 1.40, Pasteura 5 at 14:15

Jerzy Lewandowski (IFT UW)

BMS like symmetries of non-expanding horizons, corresponding charges and fluxes

room 1.40, Pasteura 5 at 14:15

Flavio Nogueira (IFW Dresden)

Bosonization duality in 2+1 dimensions and deconfined quantum critical points

“Two-dimensional quantum systems with competing orders can feature a deconfined quantum critical point, yielding a continuous phase transition that is incompatible with the Landau-Ginzburg-Wilson (LGW) scenario. The latter predicts instead a first-order phase transition. Deconfined criticality is caused by the LGW order parameter breaking up into new elementary excitations at the critical point. Canonical candidates for deconfined quantum criticality are quantum antiferromagnets with competing magnetic orders, captured by the easy-plane CP1 model. A delicate issue however is that numerics indicate the easy-plane CP1 antiferromagnet to exhibit a first-order transition. We will explore the intricate critical behavior of this model through a bosonization version of particle-vortex duality and demonstrate an overlooked critical regime in the dual model. We will show that an additional topological Chern-Simons term in the action changes this picture completely in several ways. We will find that the topological easy-plane antiferromagnet undergoes a second-order transition with quantized critical exponents. Moreover, a particle-vortex duality naturally maps the partition function of the Chern-Simons easy-plane antiferromagnet into one of massless Dirac fermions. This Bosonization duality scenario adds a new duality to the so called duality web.

room 1.40, Pasteura 5 at 14:15

Paweł Zin (NCBJ)

Non-existence of causal classical electrodynamics of point charged particles

A consistent causal theory of point charged particles (for example electrons) interacting with electromagnetic field is not known. The formulations presented so far give unphysical particle behavior. In my talk I will prove that the causal classical electrodynamics of point charged particles does not exist.

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 the years by Brunetti, Duetsch, Fredenhagen, myself and many others. This approach allows one to mathematically describe physically 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.

join us at 14:15

Bilal Cantürk (Sabanci University)

Generalizing the quantification of information

A statistical approach to the second law of thermodynamics leads to an expression in terms of probabilities (Boltzmann-Gibbs-Shannon entropy). On the other hand, a rational approach to the quantification of information led Shannon to form a function, which is formally equal to entropy up to the constant factor. From these two facts, a deep question forced itself to the mind of science: What is the relationship between information and energy? This question can be implicitly divided into two questions:
1) What is the general quantification of information?
2) What is the general relationship between information and energy?
I will present a survey of the first question and some links to the second question in the scope of the quantum measurements that are provided by mutually unbiased bases (MUBs) (Wootters & Fields, 1989) and symmetric informationally complete positive operator-valued measures (SIC-POVMs) (Renes et al., 2004).

https://us02web.zoom.us/j/82750263552?pwd=ZXB6dktLVlg3VDM3N2UwWnYzMnRrZz09
Meeting ID: 827 5026 3552
Passcode: 006674

join us at 14:15

Paweł Duch (UAM Poznan)

Infrared problem in relativistic QED

I will present a proposal for a rigorous construction of the scattering matrix in perturbative relativistic quantum electrodynamics. The construction uses adiabatic switching of the interaction and is inspired by ideas from the modified scattering theory in quantum mechanics. The constructed scattering matrix is defined in the standard Fock space and is translationally invariant as well as gauge invariant. However, the physical interpretation of states in the Fock space and the representation of the group of spacetime translations acting in this space are nonstandard.
Zoom link: 872 5064 1990
Passcode: 117994

Link: https://us02web.zoom.us/j/87250641990?pwd=RTNsQlVsUkhuRkVQc3hIZ3VVT3Fudz09

join us at 17:00

Joseph C. Schindler (UC Santa Cruz)

Penrose diagrams for explicit models of black hole evaporation

(joint seminar with UJ and UAM)

Though a full description of black hole radiation may require quantum gravity, many analyses of BH evaporation still involve, either implicitly or explicitly, key assumptions about some classical BH spacetime, often expressed in the form of (Penrose) spacetime diagrams. In this talk we discuss how such diagrams can be exactly generated for specific models - providing detailed depictions of both local and global structure - and ask what can be learned by doing so. We compare naive models to those approximating a semiclassical back reaction, as well as comparing singular and curvature-regulated models. We then consider implications for various unitarity questions including long term and Page time unitarity, and identify some open questions for further discussion.

Link: https://us02web.zoom.us/j/89278576239?pwd=NGxSVCtibTcwN0Rzc016YmkxNWF2Zz09
Meeting ID: 892 7857 6239
Passcode: 478557

room 1.40, Pasteura 5 at 14:15

Jan Kwapisz (FUW)

Renormalization group techniques: perturbative and the Wilsonian viewpoint

In the talk, I discuss how the renormalization group stems from the S-matrix in the perturbative quantum field theory. Then I turn to the complementary Wilsonian approach of integrating out the high momenta modes in the path integral. I illustrate it on the 1/r2 potential model in quantum mechanics. I briefly review the functional renormalization group techniques in the context of asymptotic safety in quantum gravity. I discuss when the renormalization scale can be identified with the energy scale of the process. I propose criteria for running in terms of amplitudes. Finally I show that string theory satisfies those criteria.

join us at 17:00

Jonathan Stanfill (Baylor University)

Spectral zeta functions and zeta regularized functional determinants for singular Sturm--Liouville operators

We employ a recently developed unified approach to the computation of traces of resolvents and zeta functions to compute spectral zeta functions associated with singular (three-coefficient) self-adjoint Sturm--Liouville differential expressions. We then discuss the zeta regularized functional determinant, illustrating what extends from a recent treatment of regular expressions and what remains open. As an application, we consider the generalized Bessel equation on a finite interval and a regularized singular problem.

Link: https://us02web.zoom.us/j/81774023863?pwd=eVlXR1U0Q0MvUHZWU2ZZd0lZR0NvZz09
Meeting ID: 817 7402 3863
Passcode: 346973

join us at 14:15

Alexander Stottmeister (University of Hannover)

Towards the quantum scaling limit of the Ising model

(joint seminar with UAM and UJ)

I will discuss how the scaling limit of the two-dimensional Ising model in its 1+1-dimensional incarnation, the transverse-field Ising chain, can be constructed by operator-algebraic renormalization. In this respect, I will point out some open questions concerning the convergence of the order parameter. As an application, I will explain out how this construction entails a quantum simulation algorithm for the Ising CFT.
https://us06web.zoom.us/j/89212837739?pwd=bkpYSVBjYlBZbGIyRVhlNmJmVERUQT09
Meeting ID: 892 1283 7739
Passcode: 371677

room 1.40, Pasteura 5 at 14:15

Wojciech Kamiński (IFT UW)

Quantum stress energy tensor

Wald axioms impose conditions on the quantum stress-energy tensor on curved background. They allow to identify this observable almost uniquely. However, especially in higher dimensions these conditions seems to be a bit too weak... I will explain how one can improve the situation using some results of Hollands and Wald. I will consider only free scalar field theory.

room 1.40, Pasteura 5 at 14:15

Adam Bzowski (IFT UW)

Breaking the spell of the tensor product

In my talk I will argue that the Hilbert space of excitations on top of a traversable wormhole is smaller than the tensor product of the independent Hilbert spaces of the boundary field theories. From the point of view of semiclassical physics, the decrease in the number of states is perceived as an emergent, non-local interaction stabilizing the wormhole. This presents new possibilities for models of radiating black holes. I will present a simple quantum-mechanical model, where the factorization of the Hilbert space is only approximate at low energies. I will show how quantum `weirdness' of the black holes physics follows from such models.

room 1.40, Pasteura 5 at 14:15

Jacek Wojtkiewicz, Piotr Chankowski (IFT UW)

Dilute Interacting Fermions by Effective Field Theory

Weź układ fermionów wielu.
Policzyć energię ich stanu podstawowego -- to mamy na celu.
Banały 'free' tu omijamy,
tzn. że oddziaływują -- to zakładamy.
Oraz, że fermiony niską gęstość mają.
To znaczy, że praktycznie swobodnie się poruszają,
i tylko z rzadka się zderzają.

To sprawia, że własności rozproszeniowe są tu fundamentalne;
dzięki nim, rachunki nie najtrudniej są wykonalne,
i wgląd w własności układów wieloelektronowych
można uzyskać z dość prostych rachunków QFTowych;
co innymi sposoby jest wprawdzie możliwe,
ale na pewno o wiele bardziej upierdliwe.
Powyżej naszkicowane tu przedstawić zamierzamy,
Mając nadzieję, że Waszą uwagę poprzyciągamy.

We consider the system of spin one-half fermions, interacting by a two-body repulsive short-range potential. We assume that their density is sufficiently low. We present the perturbativecalculation, within Effective Field Theory, of the second-order correction to ground-state energy in the case of a nonzero polarization, i.e. for non-equal densities of spin-up and spin-down particles. We also present results for spontaneous magnetization to show that the inclusion of the second-order term changes this phase transition from the second one intothe first order one.

room 1.40, Pasteura 5 at 14:15

Miłosz Panfil (IFT UW)

Local density approximation in cold atomic gases

Local density approximation is a standard technique of studying trapped atomic gases. In this talk I will explore its limitations by considering the 1d Bose gas. The 1d Bose gas, modelled by the Lieb-Liniger Hamiltonian is, in the absence of the trap, exactly solvable. We will use this exact solution to build up a perturbative expansion in the trapping potential. This is a novel approach to this problem, as the perturbed model is already a strongly interacting theory and computation of the perturbation series relies on knowledge of multi-point correlation functions. Recent advances in thermodynamic form-factors and generalized hydrodynamics provides tools to study such correlators in the relevant regime. With this approach we find an intuitive picture of the local density approximation and a precise estimation of its error.

join us at 14:15

Bogdan Damski (IFT UJ)

Angular momentum of the electron in covariantly quantized electrodynamics

I will start the talk with a brief discussion of not-so-intuitive expressions for angular momentum operators of the covariantly quantized electromagnetic field. I will then discuss radiative corrections to various components of angular momentum of the electron (e.g. spin and orbital components associated with fermionic and electromagnetic degrees of freedom). The reported results come from one-loop calculations performed in the general covariant gauge. Technical aspects of these studies, such as a not-so-obvious Pauli-Villars-like regularization of the calculations, will be commented upon.

join us at 17:00

Yoh Tanimoto (Tor Vergata)

Unitary modules and conformal nets associated with the W_3-algebra with c >= 2

(joint seminar with UJ and UAM)

The W_3-algebra is a higher spin extension of the Virasoroalgebra. We construct a conformal net associated with each of thevacuum modules of the W_3 algebra. We show the strong locality offields by a new technique involving local energy bounds.

https://us06web.zoom.us/j/81108127548?pwd=eHVvblMvMmRja3NJdVNnSnowUmVndz09
(Meeting ID: 811 0812 7548 Passcode: 992864)

room 1.40, Pasteura 5 at 14:15

Joseph C. Schindler (UC Santa Cruz)

The statistical mechanical entropy of quantum correlations

The well known connection between coarse-graining and statistical thermodynamics has recently been given a very precise formulation in terms of "observational entropy'', providing a useful notion of quantum entropy both in and out of equilibrium. In this talk I will describe how this approach gives rise to a family of measures of quantum correlation and entanglement, by minimizing observational entropy over different sets of local operations, and discuss the role of these correlations in non-equilibrium thermodynamics. The talk relates to arXiv:2005.05408.Zoom Meeting ID: 817 7402 3863 Passcode: 346973

join us at 14:15

Nick Manton (DAMTP, Cambridge)

Skyrmions, Topology and Instantons

(joint seminar with UJ and UAM)

Skyrmions are solitons in three space dimensions, constructed from a nonlinear pion field. I will discuss their basic properties, including their topological stability, and show examples. Instantons are solitons in four space dimensions, constructed from an SU(2) gauge field. I will show how Skyrmions can be approximated in terms of exact instantons, and instantons can be approximated in terms of exact Skyrmions.

https://zoom.us/j/3135628941?pwd=a3BQT3d2QnErbXlBWmxyV2h1clBSdz09
(Meeting ID: 313 562 8941 Passcode: 254367)

room 1.40, Pasteura 5 at 14:15

Piotr Kucharski (Caltech)

Knots, quivers, and quantum field theory

The knots-quivers correspondence uses the language of quantum field theory to connect two very different branches of mathematics: low-dimensional topology and quiver representation theory. The fist part of my talk will focus on an intuitive way of understanding what this correspondence is. Then I will present its generalisations and applications which make the whole story even more interesting.

room 1.40, Pasteura 5 at 17:00

Błażej Ruba (Uniwersytet Jagieloński)

Holomorphic family of Dirac-Coulomb Hamiltonians

It is a classic fact that the Dirac Hamiltonian with Coulomb potential is essentially self-adjoint only for atomic numbers Z up to 118. In the range 119 < Z < 137 essential self-adjointness is lost, but physically distinguished self-adjoint extensions exist. I will discuss how these issues can be understood by constructing a holomorphic family of Dirac-Coulomb operators. These operators depend on charge and angular momentum parameters (both allowed to be complex) and a boundary condition at the origin. Their spectral properties will be described. Another perspective on the problem of self-adjoint extensions is offered by the analysis of scaling action. With mass parameter put to zero, one obtains formally homogeneous differential operators, whose domains of self-adjointness are acted upon by the scaling group. Distinguished extensions are the infrared attractive fixed points, while for Z above 137 the scaling action becomes periodic. If time permits, I will also review separation of variables for Dirac Hamiltonian in any dimension.

The seminar will start at 17.00 (CET).
https://us02web.zoom.us/j/81774023863?pwd=eVlXR1U0Q0MvUHZWU2ZZd0lZR0NvZz09
(Meeting ID: 817 7402 3863, Passcode: 346973)

room 1.40, Pasteura 5 at 14:15

Krzysztof Byczuk (IFT UW)

Basic definition of superconductors

In this pedagogical seminar I will discuss how to define and identify superconductors. No new original results will be presented. However, discussed results during the talk are not included in standard monographs and are scattered in the literature. My aim is to collect them in one lecture.