microseminar
informal seminar of Doppler Institute
on quantum theory and related topics and methods,
usually
on Thursdays at 10.30 a.m. in Rez,
on the territory of the
Department of Theoretical Physics
of the
Nuclear Physics Institute.
Enthusiastic visitors and/or speakers are always
welcome.
FORTHCOMING SESSION:
| Place: | OTF seminar room (second floor) |
| Date: | |
| Time: | 10:30 a.m. (20 minutes + questions) |
| Speaker: |
|
| Title: |
|
Abstract: | We show that the one-dimensional Dirac operator with quite general point interaction may be approximated in the norm resolvent sense by the Dirac operator with a scaled regular potential of the form proportional to a suitable 2 by 2 matrix. We prove that the point interaction limit does not depend on the particular choice of regular potential as long as it integrates to a constant value. Preprint available: arXiv:1904.01061 [math-ph] |
ARCHIVE:
| Date and time: | Thursday, November 1st, 2018 |
| Speaker: | Kishore Thapliyal (RCPTM, Joint Laboratory of Optics [Palacky University and Inst. of Phys. of CAS], Olomouc) |
| Title and abstract: | Quantum Zeno effect and PT symmetry in optical systems |
Quantum Zeno effect is the inhibition of evolution of a quantum system on repeated measurements, while in contrast, enhancement in evolution due to repeated measurements is called quantum anti-Zeno effect. An analogue of the quantum Zeno effect is studied as the effect of a part of a system - called probe - to enhance/inhibit the evolution of the rest of the system it is continuously interacting with. Here, we have shown that quantum Zeno and anti-Zeno effects can be observed in a set of optical systems [1 - 3]. Specifically, nonlinear optical couplers [1, 2] and coupled cavities [3] form such systems where one waveguide or cavity is assumed as probe, and the effect of its presence on the dynamics of the other waveguide gives signatures of quantum Zeno and anti-Zeno effects. We have also tried to analyze the interplay between quantum Zeno effect and the parity-time symmetry (or its breaking) in the coupled cavities, a lossy and a gainy each [3]. The present study revealed that with different parameters of the physical systems of interest, and input fields a transition between quantum Zeno and anti-Zeno effects can be controlled, which independently also play an important role in the PT symmetry properties of the system of interest [2, 3].
References: [1] K. Thapliyal, A. Pathak, B. Sen, and J. Perina, Phys. Rev. A 90, 013808 (2014) [2] K. Thapliyal, A. Pathak, and J. Perina, Phys. Rev. A 93, 022107 (2016). [3] J. Naikoo, S. Banerjee, K. Thapliyal, and A. Pathak, Under preparation (2018) |
| Date and time: | Thursday, August 9th, 2018 |
| Speaker: | Ryan Plestid (McMaster University, Hamilton, Canada) |
| Title and abstract: | Point Particle Effective Field Theory as a Tool for Singular Potentials | Interactions between a small compact object (hereafter called the ``source'') and a ``bulk'' field of interest occur generically in physics with examples including finite charge as in electrostatics, and the hydrogen atom. Often, one is interested only in long-distance observables whose only underlying degrees of freedom are contained within the bulk fields. Consequently, it is desirable to be able to describe the system's behaviour on long length scales in terms of *only *the bulk fields of interest. Point Particle Effective Field Theory (PPEFT) achieves this goal by parameterizing the influence of the source on the bulk fields of interest in terms of an action localized at the location of the source, but which is composed only of bulk fields. The multipole expansion of electrostatics is shown to be a special case, however the method is general and can be applied in other, less familiar settings such as a Schrodinger field. We identify a natural power counting scheme that predicts which interactions will dominate the long-distance behavior for *any *source. As is typical in EFTs, short-distance singularities emerge, and must be regulated and subsequently renormalized. Focusing on the example of an atom interacting with a small-compact object via an inverse square potential, I will describe our real-space regulator method, and its assosciated renormaliztion group flows. |
| Date and time: | Friday, July 20th, 2018, 12:30 p.m. (triple length talk) , |
| Speaker: | Konstantin G. Zloshchastiev (Durban University of Technology) |
| Title and abstract: | Logarithmic superfluid and its application in a theory of physical vacuum | The physical vacuum is viewed as the background quantum liquid in which dissipation processes are suppressed. This leads to the spatial isotropy and inviscid flow, which make the Michelson-Morley-type measurements insensitive to such system. While being fundamentally non-relativistic, logarithmic superfluid allows in the low-momentum (so-called ``phononic'') limit small excitations obeying the Lorentz symmetry [arXiv:1108.0847]. Therefore, for an observer operating with such small excitations, their fluid-theoretical description is equivalent to a geometrical description in terms of the spacetime with non-vanishing Riemann curvature, whereas these excitations are observed as relativistic particles [arXiv:0912.4139]; in other words, the relativity postulates are recovered in this special ``phononic'' limit. However, the ``full'' observer sees the superfluid flow embedded in 3D Euclidean space, and the relativistic notions, such as a particle or spacetime, are no longer fundamental but can be useful as an approximation, up to a certain threshold value of momentum or energy. It is demonstrated that the logarithmic nonlinearity can cause also the spontaneous symmetry breaking and mass generation phenomena [arXiv:1204.6380]. The related issues, such as the vacuum Cherenkov radiation [arXiv:1003.0657], extended particles and Q-balls [arXiv:1611.02105], induced scalar-tensor gravity, black holes and cosmology, are discussed as well. The studies suggest that the theory of gravity, both classical and quantum, can be viewed as a subset of the theory of physical vacuum, where the latter is viewed as a condensed-matter phenomenon. |
| Date and time: | Wednesday, November 1st, 2017 , |
| Speaker: | Peter Schlosser (TU Graz) |
| Title and abstract: | Lieb-Thirring type inequality for delta-potentials supported on the hyperplane | The selfadjoint realisation of the differential expression $-\triangle + \alpha \delta_\Sigma$ is defined by a sesquilinear form and the First Representation Theorem. It describes a delta-shaped potential supported on the (d . 1)-dimensional hyperplane $\Sigma$, where the interaction strength $\alpha$ is allowed to be any (not necessarily bounded) function in some $L^p(\Sigma)$ space. With the technique of quasi boundary triplets it is possible to find an equivalent representation of this operator via boundary values as well as a Krein resolvent formula, which allows to calculate the essential spectrum explicitly. For the discrete spectrum a Lieb-Thirring type inequality is proven, which shows, that the sum over all discrete eigenvalues, to some arbitrary (positive) power, is bounded by the $L^p(\Sigma)$-norm of the negative part of the potential. One can even generalise the above setting and shift the potential $\alpha$ by some negative constant. Again it is possible to calculate the essential spectrum explicitly and to derive a Lieb-Thirring type inequality. But in this case the order of convergence of the discrete eigenvalues towards the bottom of the essential spectrum is different. |
| Date and time: | Wednesday, October 4th, 2017, 10:30 a.m. |
| Speaker: | Axel Perez-Obiol (Department of Theoretical Physics, NPI CAS, Rez) |
| Title and abstract: | Twisting and shrinking of carbon nanotubes at zero temperature | Deformations of single-wall carbon nanotubes are investigated within the tight-binding model with deformation-dependent hopping energies. We show that the nanotubes tend to twist and shrink spontaneously at zero temperature. The explicit values of the deformation parameters are computed for a wide range of nanotubes with varying diameter and chirality. The changes of the spectral gap associated with the spontaneous deformation are shown to depend on the chirality of the nanotubes. |
| Date and time: | Wednesday, March 15th, 2017, 10:30 a.m. |
| Speaker: | Petr Jizba (Department of Physics, FNSPE, Czech Technical University in Prague) |
| Title and abstract: | A new class of entropy-power-based uncertainty relations |
The concept of entropy power will be used to derive a new one-parameter
class of information-theoretic uncertainty relations for pairs of observables in an
infinite-dimensional Hilbert space. This class constitute an infinite tower of
higher-order cumulant uncertainty relations, which allows in principle to
reconstruct the underlying distribution in a process that is analogous to quantum
state tomography. I will illustrate the power of the new class by studying
Schroedinger cat states and the Cauchy-type heavy-tailed wave function. Finally, I
try to cast some fresh light on the black hole information paradox.
Related works: [1] P. Jizba, J.A. Dunningham and J. Joo, Role of information theoretic uncertainty relations in quantum theory, Annals of Physics 355 (2015) 87 [2] P. Jizba, J.A. Dunningham, A. Hayes and Y. Ma, A new class of entropy-power-based uncertainty relations, Phys. Rev. E 93 (2017) 060104(R) [3] P. Jizba, H.Kleinert and F.Scardigli, Uncertainty Relation on World Crystal and its Applications to Micro Black Holes, Phys. Rev. D81 (2010) 084030 |
| Date and time: | Wednesday, March 8th, 2017, 10:30 a.m. |
| Speaker: | Ananya Ghatak (Indian Institute of Science, Bangalore, India) |
| Title and abstract: | Exotic features of pseudo-Hermitian systems |
Recently the study of certain classes of non-Hermitian quantum systems attracted lots of interest as one can have fully consistent quantum theories by restoring the Hermiticity and by upholding the unitary time evolution for such systems in a modified Hilbert space. In this talk we will discuss some of the exciting recent developments with pseudo Hermitian and particularly PT-symmetric Hamiltonians. Systems with such Hamiltonians are adoptable in quantum optics, condensed matter physics and many other branches of physics and science.
Note: After the talk we continued with poster minisession over freshly submitted report "PT-symmetric non-Hermitian superconductor" by A.G. and Tanmoy Das (IISc Bangalore) |
| Date and time: | Tuesday, October 25th, 2016, 12:30 p.m. |
| Speaker: | Hafida Moulla (University of Constantine 1, Constantine, Algeria) |
| Title and abstract: | The q-deformed harmonic oscillator |
It is known that the q-deformed version of the operator
of "particle position" - which is an
observable quantity - is not selfadjoint in L2(R). The
resolution of the paradox is provided using the standard
three-Hilbert-space theory
due to
Freeman Dyson. Firstly, the inner product
in the Hilbert space of states is properly
redefined.
Secondly, a few consequences are discussed via the
q-deformed version of the usual harmonic oscillator.
Note: The language of the talk was French, the transparencies were in English. |
| Date and time: | Tuesday, October 11th, 2016, 12:30 p.m. |
| Speaker: | Ilhem Leghrib (University of Constantine 1, Constantine, Algeria) |
| Title and abstract: | Swanson model |
A q-deformed generalization of the well known non-Hermitian Swanson's
Hamiltonian is introduced and studied. In the dynamical regime of small
deformations (i.e., with q close to one) the methods of perturbation
theory are employed.
Note: The language of the talk was French, the transparencies were in English. |
| Date and time: | Thursday, August 18th, 2016, 2:30 p.m. |
| Speaker: | Ondrej Turek (OTF UJF in Rez and BLTP JINR in Dubna, Russia) |
| Title and abstract: | A generalization of the circulant Hadamard conjecture |
The circulant Hadamard conjecture says that circulant Hadamard matrices
exist only of order n=1 and n=4. The conjecture, which dates back to
a book of Ryser (1963), is partially proved in the symmetric case
(Johnsen 1964). The general case, however, remains open to this day.
In 1976, Stanton and Mullin showed that circulant conference matrices
exist only of order n=2. With regard to their result, we consider
circulant matrices C of order n>1 with diagonal entries $d \geq 0$,
off-diagonal entries $\pm 1$ and mutually orthogonal columns. Matrices
C generalize circulant Hadamard (d=1) and conference (d=0)
matrices. We demonstrate that the parameter d and the order of C
obey the relation n=2(d+1), whenever d is different from an odd
integer, as well as when C is symmetric. The formula n=2(d+1)
generalizes the theorems of Stanton, Mullin and Johnsen and reveals a
suprising connection between circulant Hadamard and conference matrices.
Furthermore, we conjecture that the relation n=2(d+1) is valid also
when d is an odd integer, which generalizes the circulant Hadamard
conjecture.
The talk was based on a joint work with D. Goyeneche. |
| Date and time: | Tuesday, June 21st, 2016, 10:30 a.m. |
| Speaker: | Artur Ishkhanyan (Institute for Physical Research of the National Academy of Sciences of Armenia, Ashtarak) |
| Title and abstract: | Heun functions and Schroedinger equation | We shall review the cases for which the Schroedinger equation is solved in terms of general and confluent Heun functions. We present the possible choices for the coordinate transformation that provide energy-independent potentials that are proportional to an energy independent continuous parameter and have a shape independence of that parameter. We present several examples of explicit solutions for the latter potentials. |
| Date and time: | Wednesday, June 1st, 2016, 14:30 a.m. (triple length) |
| Speaker: | Alexander Turbiner (Stony Brook and UNAM, Mexico) |
| Title and abstract: | 3-body quantum Coulomb problem: where we are | Current status of 3-body Coulomb problem of charge Z and two electrons (Z; e; e): hydrogen ion H-, helium atom, lithium ion, $H^+_2$ ion etc, is given. Major emphasis is given to a question of stability vs. Coulomb charge Z and to analytic structure of the ground state energy vs. Z. Celebrated 1/Z expansion is reviewed. Two critical charges, physical (corresponding to phase-transition type discontinuity) and unphysical (with associated square-root branch point) are described and calculated. The 2nd excited, weakly-bound state of $H^-$ is predicted. |
| Date and time: | Thursday, January 21st, 2016, 10:30 a. m. |
| Speaker: | Vladimir Lotoreichik (OTF) |
| Title and abstract: | A spectral isoperimetric inequality for cones |
Spectral isoperimetric inequalities are one of the most famous issues in spectral geometry, the first rigorous results dating almost a century back to the papers of {Faber} and {Krahn}. Recently such inequalities appeared in the context of Schr\"odinger operators with singular potentials used as models of `leaky quantum wires' and similar systems. In particular, for the 2-D Schroedinger operator with a $\delta$-potential of a fixed strength supported on a loop of a given length it was shown by {Exner}, {Harrell} and {Loss} that its principal eigenvalue is maximal when the loop is a circle. The corresponding problem in 3-D is more involved. For closed simply connected surfaces of a fixed area the sphere gives a local maximum of the ground-state eigenvalue, however, the result does not have a global validity.
Nevertheless, there are 3-D Schroedinger operators with singular interactions supported on surfaces for which one is able to derive a spectral isoperimetric inequality that holds not only locally. The aim of my talk is to discuss one such class considered in our preprint (arXiv:1512.01970). The surfaces in question are of a conical shape, both finite and infinite. The proofs rely on the Birman-Schwinger principle and on the fact that circles are unique minimisers for a class of energy functionals. The main novel idea consists in the special choice of the test function for the Birman-Schwiner principle. Joint work with Pavel Exner. |
| Date and time: | Thursday, January 7th, 2016, 13:30 a.m. (irregular time) |
| Speaker: | Ondrej Turek (OTF UJF in Rez and BLTP JINR in Dubna, Russia) |
| Title and abstract: | The effect of edge lengths ratio on the spectrum of a hexagonal lattice |
We analyze the spectrum of a Laplacian operator on a dilated honeycomb lattice. The lattice is assumed to be dilated along its axis of symmetry and supporting $\delta$ potentials of strength $\alpha \neq 0$ in its vertices. It turns out that the qualitative properties of the spectrum depend on number-theoretic properties of edge lengths ratio $\theta$. We will show that the number of spectral gaps is infinite for any rational or well approximable $\theta$, whereas there are only finitely many gaps in the spectrum if $\theta$ is badly approximable and the potential strength $\alpha$ in the vertices is small compared to the Markov constant of $\theta$.
This talk is based on joint works with P. Exner. |
The archive of the older microseminars:
The list of talks during 2012 - 2015
The list of talks during 2008 - 2011
The list of the talks during 2008
A compactified list of the speakers during 2008
The list of the talks during 2007
A compactified list of the speakers during 2007
The list of the talks during 2006
A compactified list of the speakers during 2006
PS: in parallel, nested seminars of the similar type may be also sought on the webpages of our local
microconferences
devoted to the analytic an algebraic methods in physics
Info for potential/interested external speakers:
| you would be always welcome by: | all of us |
| you may choose any date and time | though Thursdays on 10.30 are preferred |
and any subject related to
|
|
| you should book your term of talk: | not later than 2 or 3 days in advance |
| your talk's length should be | 20 minutes |
| time for subsequent questions: | unlimited |
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