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 14:15

Paweł Kasprzak (KMMF)

Introduction to compressed sensing theory and practice

The aim of this talk is to give a gentle introduction to compressed sensing (CS). In particular the main problem leading to the development of CS will be described and the RIP - condition will be discussed. Finally I will describe three different classes of algorithms (IST, IRLS, OMP) yielding the solution of the main CS - problem.

room 1.40, Pasteura 5 at 14:15

Przemysław Małkiewicz (NCBJ)

“Quantum dynamics of Hamiltonian constraint systems”

The lack of external and fixed time is encoded into the canonical formalism of general relativity by means of the Hamiltonian constraint. The lack of time does not imply the lack of evolution but rather brings to the fore the role of internal clocks which are some largely arbitrary internal degrees of freedom with respect to which the evolution of timeless systems can be described. I will take this idea seriously and try to understand what it may imply for quantum mechanics when the fixed external time is replaced by arbitrary internal clocks.

room 1.40, Pasteura 5 at 14:15

Chris Fewster (University of York)

On preferred states for quantum fields in curved spacetimes

The vacuum state of Minkowski space quantum field theory is distinguished as a state of maximal symmetry. General curved spacetimes have no nontrivial symmetry and therefore lack an obvious candidate vacuum state. Nonetheless, one might wonder whether there is still a way of selecting a preferred state. I will discuss various aspects of this issue, describing a general no-go theorem that excludes the existence of a local and covariant choice of preferred state and also results due to Verch and myself, and Brum and Fredenhagen, concerning a recent class of states originally introduced by Afshordi, Aslanbeigi and Sorkin under the name "SJ state", including an extension to Dirac fields in a joint paper with Lang.

room 1.40, Pasteura 5 at 14:15

Jan Dereziński (IFT UW)

Toy model of renormalisation group

room 1.40, Pasteura 5 at 14:15

Rafał Demkowicz-Dobrzański (IFT UW)

Exact results in Quantum Metrology

Quantum metrology investigates the possibility of exploiting quantum features such as coherence and entanglement to boost the precision of measurements of time, length etc.From a more mathematical perspective it is a theory on the optimal strategies in discriminating quantum channels. I will give a brief review of the most interesting result from the field and connect abstract concepts such as geometry of completely-positive maps and the quantum Master equation with real life problems such as fundamental limits to stability of atomic clocks and sensitivity of gravitational wave detectors.

room 1.40, Pasteura 5 at 14:15

Andrzej Görlich (UJ)

Introduction to Exact Renormalization Group

In this talk, I will introduce an Exact Renormalization Group proposed by Polchinski in Nucl. Phys. B231 (1984) 269. Its principles are very general and should apply to any system whose symmetries are preserved by a momentum-space cutoff. As an example, I will consider a four-dimensional \phi^4 theory with a momentum cutoff. After identifying relevant and irrelevant operators, the exact renormalization group equations describing the cutoff dependence of the effective Lagrangian will be derived.

room 1.40, Pasteura 5 at 14:15

Grzegorz Łach (IFT UW)

Non-adiabatic Perturbation Theory

The solving of Schroedinger equation for molecular systems is usually done by first applying the Born-Oppenheimer approximation. I will describe a method, based on the idea of effective Hamiltonian, which does allow for a systematic calculation of corrections beyond the Born Oppenheimer approximation.

room 1.03, Pasteura 5 at 14:15

Mehdi Assanioussi (IFT UW)

Approximation methods for the dynamics in deparametrized LQG models

An important aspect in understanding the dynamics in LQG in the context of deparametrized models is to obtain a sufficient control on the quantum evolution generated by a given Hamiltonian operator. More specifically, we need to be able to compute the evolution of relevant physical states and observables with a relatively good precision. In this talk, I present an approximation method to deal with the physical Hamiltonian operators in the context of (time) deparametrized LQG models, and discuss two known models as examples. This method is using standard time-independent perturbation theory to define a perturbative expansion of a Hamiltonian operator, the small perturbation parameter being determined by the Barbero-Immirzi parameter. This method allows us to approximate transition amplitudes and to evolve expectation values of geometrical operators over a certain time interval.

room 1.40, Pasteura 5 at 14:15

Krzysztof Meissner (IFT UW)

Conformal anomalies

The presence of conformal anomalies in gravitational theories can lead to observable modifications to Einstein's equations via the induced anomalous effective actions. The fact that no such effects have been seen in cosmological or gravitational wave observations therefore imposes strong restrictions on the field content of possible extensions of Einstein's theory: all viable theories should have vanishing conformal anomalies. The 'miraculous' cancellation of conformal anomalies for N-extended supergravities will be discussed.

room 1.40, Pasteura 5 at 14:15

Jacopo De Nardis (IFT UW)

Emerging non-equilibrium dynamics of integrable systems

We review application of integrability to non-equilibrium problems showing how the non-equilibrium dynamics of local observables is fixed by all the irreducible representations of the underlying symmetry of the model, that eventually produce quasi-local conserved operators. We show how to include such operators in a reduced density matrix and how they also allow for an exact description of the spin conductivity in spin chains and how this is usually a non-continuos function of the interaction strength.

room 1.40, Pasteura 5 at 14:15

Jochen Zahn (Universität Leipzig)

Local gauge covariance and global anomalies

I review the locally gauge covariant formulation of QFT in background gauge fields, which is a generalization of the locally covariant framework for QFT on curved space-times. The principle of perturbative agreement, introduced by Hollands & Wald, is applied to gauge background fields and a form of the Adler-Bardeen theorem is derived. Finally, these concepts are applied to a discussion of global anomalies. The latter part is based on joint work with A. Schenkel.

room 1.40, Pasteura 5 at 14:15

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no seminar this week

room 1.40, Pasteura 5 at 14:15

Krzysztof Wohlfeld (IFT UW)

On the relations between the basic models of the correlated electrons systems on a lattice

In the first part of the talk I will discuss how the basic and best known models of the correlated electron systems are related to each other: Hubbard, t-J [1], Heisenberg, and Kugel-Khomskii spin-orbital models. Next, I will show the 1:1 correspondence between the spectral function of the t-J model and a particular Kugel-Khomskii spin-orbital model [2]. This latter feature has important consequences for the understanding of the recent spectroscopic experiments performed on transition metal oxides.[1] J. Spalek was recently awarded the FNP prize for the "distinguished contribution to the world of physics in 1977 when he derived for the first time the so-called t-J model" [K. A. Chao, J. Spalek, A. M. Oles, J. Phys. C 10, L271 (1977)].[2] Phys. Rev. Lett. 107, 147201 (2011); Phys. Rev. B 91, 165102 (2015).

room 1.40, Pasteura 5 at 14:15

Jacek Wosiek (Jagiellonian University)

Beyond complex Langevin equations: from simple examples to positive representation of Feynman path integrals directly in Minkowski time

Stochastic quantization is a well known approach which replaces ensemble averages by averaging over a suitable stochastic process. It was designed and proved for positive densities, i.e. real, euclidean actions. However Langevin process can be also defined for complex actions, raising expectations for statistical averaging over complex "distributions". This has attracted a new wave of interest after recent reports of successful study of quantum chromodynamics at finite chemical potential. Nevertheless there is no proof of convergence in the complex case, and indeed the evidence for success is limited.In this talk we will circumvent above problems by introduction of additional variables and direct construction of pairs of corresponding (i.e. complex and positive) weights. As an application, the well known solution for a complex Gaussian distribution will be generalized to arbitrary complex slope. This opens a way to construct positive representations of path integrals directly in Minkowski time and will be done in the second part of the talk.Then some applications to simple, classic quantum systems will be presented. Finally a striking physical interpretation of the new structure will be suggested, albeit with due caution.

room 1.40, Pasteura 5 at 15:15

Hermann Nicolai (IFT UW)

Cosmobilliards

According to the BKL conjecture, Einstein's equations exhibitremarkable simplifications in the limit towards a spacelike (cosmological)singularity. At the same time there emerges evidence for a huge `hiddensymmetry' of indefinite Kac-Moody type that is closely related to theduality symmetries that have appeared in supergravity and superstringtheories. This lecture will provide a survey of these results at anintroductory level.

room 1.40, Pasteura 5 at 14:15

Chun-Yen Lin (IFT UW)

Transition Amplitudes with Quantum Dynamical Spacetimes

Using an important cosmological model, I will formulate the issues ofobtaining unitary evolution from the transition amplitudes in quantumgravity, in the contexts of two major canonical approaches — the reducedphase space approach and the Dirac approach. I will also present theapplication of a new method, which aims to solve these issues by unifyingthe two approaches.

room 1.40, Pasteura 5 at 14:15

Daniel Siemssen (IFT UW)

Propagators

The Klein-Gordon equation has several interesting and relevant propagators (also called Green’s functions or two-point functions): the forward/backward propagator, the Pauli-Jordan propagator, the Feynman propagator, the Wightman two-point function. In this talk I will discuss an approach to construct propagators on curved spacetimes. This approach can also be applied for non-smooth metrics and when external electromagnetic fields are present. For static spacetimes, I will show that the Feynman propagator can be constructed as the limit of the resolvent of the Klein-Gordon operator. I will then argue that this construction can be generalized to some non-static spacetimes.

room 1.40, Pasteura 5 at 14:15

Krzysztof Wohlfeld (IFT UW)

On the relations between the basic models of the correlated electrons systems on a lattice

In the first part of the talk I will discuss how the basic and best known models of the correlated electron systems are related to each other: Hubbard, t-J [1], Heisenberg, and Kugel-Khomskii spin-orbital models. Next, I will show the 1:1 correspondence between the spectral function of the t-J model and a particular Kugel-Khomskii spin-orbital model [2]. This latter feature has important consequences for the understanding of the recent spectroscopic experiments performed on transition metal oxides. [1] J. Spalek was recently awarded the FNP prize for the "distinguished contribution to the world of physics in 1977 when he derived for the first time the so-called t-J model" [K. A. Chao, J. Spalek, A. M. Oles, J. Phys. C 10, L271 (1977)]. [2] Phys. Rev. Lett. 107, 147201 (2011); Phys. Rev. B 91, 165102 (2015).

room 1.40, Pasteura 5 at 14:15

Maciej Nieszporski (KMMF UW)

Proper discretizations of differential equations

Replacement of differential operators with difference operators in a differential equation is often referred to as naive discretization.I will present some examples where it seems we are not naive.

room 1.40, Pasteura 5 at 14:15

Paweł Jakubczyk (IFT UW)

Functional renormalization group perspective on the Berezinskii-Kosterlitz-Thouless transition

I will review the functional renormalization group approach to the classical O(N) models in two and three spatial dimensions. I will discuss in some detail the specific case of N=2 and d=2, corresponding to the Berezinskii-Kosterlitz-Thouless universality class.

room 1.40, Pasteura 5 at 14:15

Michał Wrochna (Joseph Fourier University, Grenoble)

Quantum fields on asymptotically de Sitter spacetimes and their extension across the conformal horizon

In the construction of scalar quantum fields on a curved spacetime, the crucial step is to split the solution space of the Klein-Gordon equation into two parts corresponding to particles and anti-particles. The splittings need to satisfy the so-called Hadamard condition, originally formulated by Kay and Wald and incorporating the requirement that two-point functions of fields should be microlocally the same as the Minkowski vacuum. In this talk, I will present a solution to this problem on a class of asymptotically de Sitter spacetimes, derived in a recent joint work with András Vasy and relying on propagation estimates at radial sets. The crucial feature is the extendability of appropriately rescaled classical fields across the conformal horizon, to a region consisting of two asymptotically hyperbolic spaces. It turns out that non-interacting quantum fields follow the same behaviour and are uniquely determined by data in the asymptotically hyperbolic spaces.

room 1.40, Pasteura 5 at 14:15

Marcin Napiórkowski (KMMF UW)

From Many-Body Quantum Mechanics to Gross-Pitaevskii equation and beyond

Since the experimental realization of Bose-Einstein condensation (BEC) in Bose gases, it has been an ongoing challenge in mathematical physics to derive the phenomenon from the first principles of quantum mechanics. This has first been achieved in 2002 by Lieb and Seiringer for dilute, trapped systems. More recently, BEC has been proven for weakly interacting systems within the so-called mean-field limit. In my talk, I will both review existing and present recent results on the dynamics of weakly interacting Bose gases in the mean-field limit.

room 1.40, Pasteura 5 at 14:15

Antoine Géré (IFT UW)

A 3D toy model for noncommuative field theories

We look at models of noncommutative field theories (NCFT) on a particular space $\mathbb{R}^3_\lambda$. After a presentation of this particular space, we review the construction of gauge models in this framework.Then we show that natural noncommutative gauge theory models on $\mathbb{R}^3_\lambda$ can accommodate gauge invariant harmonic terms. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We perform computations at one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is then discussed.

room 1.40, Pasteura 5 at 14:15

Grzegorz Łach (IFT UW)

"Principle of the conservation of effort" and how to bypass it

During last decade it has been shown that huge variety of computational problems can be (exactly) rewritten as boolean satisfiability problems (so called SAT or #SAT problems) to which very efficient computational tools (aka SAT-solvers) exist.