We introduce a spin-chain model with dynamics consisting of a unitary circuit with discrete conformal symmetry. This model is holographically dual to a toy theory of quantum gravity in 2+1 dimensions, where certain tensor-network states correspond to classical discrete geometries. Unlike previous approaches, like holographic codes, these tensor networks and geometries evolve in time, reproducing some phenomena from general relativity. Also, these states satisfy the Ryu-Takayanagi correspondence between entanglement and geometry, but they provide much more, they contain a complete description of the bulk, including the interior of black holes, a feature that is not so transparent in standard AdS/CFT.

All lectures will take place in the seminar room 133 (Jadranska Ulica 21, new building). The schedule is

Please find the program of the 11th Trieste-Ljubljana-Zagreb meeting

Simulation of the single-particle tunneling problem by means of the Suzuki-Trotter approximation (STA) is analyzed. The target system describes a particle hopping across a chain of sites with position-dependent potential profile. The latter is assumed to be smooth and posses several local minima separated by a potential barrier, arranging a tunneling problem between the localized states in different minima. The STA error is found to manifest itself in three ways: i) perturbative energy shifts, ii) nonperturbartive renormalization of the tunneling rates, and iii) perturbative leakage of total probability to other states. In the general case, the first type of error is the most essential, as the emerging detuning of the tunneling resonance has to be compared with exponentially small tunneling rates. In absence of detuning (e.g. if the resonance is protected by symmetry), STA is found to cause exponential enhancement of the tunneling rates. The last type of error classifies the overall defect in the wave function and thus delineates the region of sufficiently weak distortion of the wave function due to STA. The conducted analysis confirms the naive criteria of applicability max{T, P } ≪ 1/δt (with T, P being the typical scales of kinetic and potential terms, respectively), while also revealing the structure of error and its actual behavior with system parameters. Analysis of the case of large Trotter step is also performed, with the main result being the reconstruction of the low-energy spectrum due to coupling between states with energy difference close to 2π/δt. The connection of the obtained results with the rigorous upper error bounds on the STA error is discussed, with particular emphasis on the reasons for the fact that these rigorous bounds are not always saturated. We also point out that the proposed problem can be directly implemented on existing quantum devices [arXiv:2012.00921]. In particular, we give a detailed description of an experimental design that demonstrates the described physics. The talk is based on the recent paper [arXiv:2312.04735].

We study the out-of-time-order correlation function (OTOC) in a
lattice extension of the Sachdev-Ye-Kitaev (SYK) model with quadratic
perturbations. The results obtained are valid for arbitrary time
scales, both shorter and longer than the Ehrenfest time. We
demonstrate that the region of well-developed chaos is separated from
the weakly chaotic region by the “front region”, which moves
ballistically across the lattice. The front velocity is calculated for
various system’s parameters, for the first time for SYK-like models.

*Aleksey Lunkin, Landau Institute Moscow*

We consider black hole linear perturbation theory in a four-dimensional Schwarzschild (anti-)de Sitter background. We describe two methods that provide the quantization condition for the quasinormal mode frequencies of the perturbation field. The first consists of using the Nekrasov-Shatashvili functions, or, equivalently, the classical Virasoro conformal blocks, to obtain the connection coefficients for the differential equation encoding the spectral problem. The second method is based on a perturbative expansion of the local solutions of the differential equation, that involves multiple polylogarithmic functions. We conclude by showing how the two methods shed light on the mathematical structure of the quasinormal mode frequencies, and discussing how they can be generalized to problems in different backgrounds, emphasizing their effectiveness.

Paolo Arnaudo, SISSA

We study localization phenomena in an SNS junction with a disordered metallic wire as its normal part. Standard description of the Josephson effect in such systems is based on the Usadel equation. However, the classical approach remains valid only while the junction is shorter than the localization length in the wire. In the opposite limit, quantum effects become important and the Usadel description is no longer valid.

We develop a general theory of the Josephson effect taking into account all localization (quantum) contributions. Our theory is based on the nonlinear sigma model and can be applied to junctions of arbitrary length including very long junctions (exceeding the localization length) when a fully quantum description is required. Applied to the Josephson effect in this limit, the theory predicts three qualitatively different regimes depending on relation between the length of the junction, superconducting coherence length, and localization length. In all these regimes, we found analytical expressions for the current-phase relation and estimates for the critical current. In particular, we demonstrate that Ambegaokar-Baratoff relation can remain valid under certain conditions even in the strongly localized limit.

Pavel Ostrovsky, Max Planck Institute Stuttgart

We consider a harmonic chain of oscillators in the presence of a disordered magnetic field. The disorder, in general, causes localization of the normal modes, due to which a system becomes insulating. However, for this system, the localization length diverges as the normal mode frequency approaches zero. Therefore, the low-frequency modes contribute to the heat transmission and the heat current goes down as a power law with the system size. This power law is determined by the small frequency behavior of some Lyapunov exponents and the heat transmission in the thermodynamic limit. We find the behavior of these two quantities and show that the power law for the current is different for zero and nonzero expectation value of the magnetic field.

*Junaid Majeed-Bhat, FMF Ljubljana

Unusual day – Friday 2pm

In the talk, I briefly discuss the present-day view of the magnetic field evolution of neutron stars and its main observational appearance. Then, I focus on the possibility of finding magnetars in binary systems of a different kind. Possible candidates include accreting neutron stars (in particular, ultra-luminous X-ray sources), gamma-ray sources, and fast radio bursts. I present a scenario in which the existence of a highly magnetized neutron star in a high-mass X-ray binary is possible at an age ~few million years.