Nonlinear evolution is not a usual phenomenon in quantum physics. It is possible to define a time-evolution for an ensemble of equally prepared systems in a somewhat unusual way: take N systems, apply an entangling unitary transformation, measure all but one of the systems and, depending on the measurement results, keep or throw away the remaining system. This procedure applied to the whole...
By extending the gauge covariant magnetic perturbation theory to operators defined on half planes, we prove that for general 2d random ergodic magnetic Schrödinger operators the celebrated bulk-edge correspondence is just a particular case of a much more general paradigm, which also includes the theory of diamagnetic currents and of Landau diamagnetism. Our main result is encapsulated in a...
We derive and discuss one- and two-dimensional models for classical electromagnetism by making use of Hadamard’s method of descent. Low-dimensional electromagnetism is conceived as a specialization of the higher dimensional one, in which the fields are uniform along the additional spatial directions. We then consider two-dimensional models for a charged spin-1/2 particle, both in the free case...
We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, fluxes of fermions into the different reservoirs, as well as the entropy production rate of the dynamics.
This is joint work with S. Andréys and R. Raquépas.
We show that for any finite-dimensional quantum systems the conserved quantities can be characterized by their robustness to small perturbations: for fragile symmetries, small perturbations can lead to large deviations over long times, while for robust symmetries, their expectation values remain close to their initial values for all times. This is in analogy with the celebrated...
We discuss the construction of the trace operator defined on Sobolev spaces over a class of infinite trees based on an identification of the abstract boundary with an Euclidean domain. This can be used to study coupling problems between objects of different dimensions. Joint work with Kiyan Naderi (Oldenburg).
Coherent laser-induced excitation processes based on timescale hierarchies offer interesting perspectives for the controlled and deterministic preparation of entangled multipartite quantum states. Greenberger-Horne-Zeilinger (GHZ) and W-states are prominent examples of such multipartite quantum states which constitute valuable resources for quantum information processing. Motivated by current...
The question of optimizing an eigenvalue of a family of self-adjoint operators that depends on a set of parameters arises in diverse areas of mathematical physics. Among the particular motivations for this talk are the Floquet-Bloch decomposition of the Schroedinger operator on a periodic structure, nodal count statistics of eigenfunctions of quantum graphs, conical points in potential energy...
The question asked in the title is addressed from two points of view:
First, we show that providing enough (term to be explained) spectral data, suffices to reconstruct uniquely generic (term to be explained) matrices. The method is well defined but requires somewhat cumbersome computations.
Second, restricting the attention to banded matrices with band-width much smaller than the...
Time in quantum mechanics, especially the non-relativistic theory has privileged position in that
unlike the Cartesian coordinates it is a parameter rather than an operator. Moreover, it is a parameter
over which we have no control: time passes and our quantum systems evolve. Yet the theory is
essentially time-symmetric (as is most of the rest of physics) so there is a sense in which...
In this talk I will present some new results on the excess charge for bosonic systems.
Reaching ultimate performance of quantum technologies requires the use of detection at quantum limits and access to all resources of the underlying physical system. We establish a full quantum analogy between the pair of angular momentum and exponential angular variable, and the structure of canonically conjugate position and momentum. This includes the notion of optimal simultaneous...
In the first part we will describe the dynamics of a quantum particle coupled to bosonic fields, in the quasi-classical regime. In this case, the fields are very intense and the corresponding degrees of freedom can be treated semiclassically. We prove that in such a regime the effective dynamics for the quantum particles is approximated by
the one generated by a time-dependent point...
Einstein in 1905, in his explanation of the photoelectric effect, postulated that light, the quintessential wave, had to possess particle-like properties. In the course of 1923-24, de Broglie, analyzing electron scattering from metal surfaces, postulated that electrons, the quintessential particles, must possess wave-like properties. In 1928, Bohr made the first attempt to reconcile the two...
The concept of divisibility of dynamical maps will be used to introduce an analogous concept for quantum channels by analyzing the simulability of channels by means of dynamical maps. In particular, this is addressed for Lindblad divisible, completely positive divisible and positive divisible dynamical maps. The corresponding L-divisible, CP-divisible and P-divisible subsets of channels are...
The Riemann zeta function ζ plays a crucial role in number theory as well as physics. Indeed, the distribution of primes is intimately connected to the non-trivial zeros of this function. We briefly summarize the essential properties of the Riemann zeta function and then present a quantum mechanical system which when measured appropriately yields ζ. We emphasize that for the representation in...
We introduce a new spectral invariant: the generalized Euler characteristic $\mathcal{E}$ [1]. The commonly used Euler characteristic i.e., the difference between the number of vertices $|V|$ and edges $|E|$ is the most important topological characteristic of a graph. However, to describe spectral properties of differential equations with mixed Dirichlet and Neumann vertex conditions it is...
Quantum technologies promise a change of paradigm for many fields of application, for example in communication systems, in high-performance computing and simulation of quantum systems, as well as in sensor technology. They can shift the boundaries of today’s systems and devices beyond classical limits and seemingly fundamental limitations.
Photonic systems, which comprise multiple optical...
