We will discuss the initial value problem given by the incompressible Navier–Stokes equations in $\mathbb{R}^3$. All known well-posedness results for this problem are in the perturbative regime and in this talk we will show numerically that the problem is ill-posed outside the perturbation regime. More precisely, we numerically construct two different solutions having the same initial datum in...
For $N$ hard-core bosons on an arbitrary lattice with $d$ sites and independent of additional interaction terms we prove that the hard-core constraint itself already enforces a universal upper bound on the Bose-Einstein condensate given by $N_{max}=(N/d)(d-N+1)$. This bound can only be attained for one-particle states $|\varphi\rangle$ with equal amplitudes with respect to the hard-core basis...
I investigate the critical dynamics of a periodically driven Bose gas. The inclusion of dissipation enables the system to reach a far-from-equilibrium steady state where the periodic drive plays an essential role. Combining the Renormalization Group (RG) and Floquet formalisms, I describe the steady state by allowing for an arbitrary number of Floquet modes to be occupied. In practice, this...
The fermionic exchange symmetry does not only imply Pauli's exclusion principle but even further constraints on fermionic occupation numbers. In particular, generalized Pauli constraints become relevant whenever they are (approximately) saturated. We explore the occurrence of such (quasi)pinning through a comprehensive analysis of an analytically solvable model (Harmonium). By analysing the...
We study the time evolution of 2-point-functions and entanglement-entropy in anisotropic and time dependent $\mathcal{N}=4$ super-Yang-Mills-theory in the large $N$ and large 't Hooft-coupling limit using AdS/CFT.
On the gravity side this amounts to calculating geodesics and extremal surfaces in the background of two colliding gravitational shockwaves, which we do numerically.
Discriminating...
Understanding electron correlations is nowadays crucial for advances in quantum electronics and nano-sciences. Quantum Monte-Carlo simulation (QMCS) methods, being highly time consuming, are limited to yield selective data points only. We here employ a Hyper-Netted-Chain-theory based approach to compute the spin-resolved pair distribution functions and static structure factors of the...
We consider Gaussian fermionic states and their entanglement properties. Among continuous variable systems Gaussian states stand out prominently, because of their simple and elegant mathematical description in terms of first and second order correlations. Moreover, the subclass of Gaussian fermionic states has the distinguished feature, that they can be mapped onto systems consisting of qubits...
We study 1D insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with N.N. hopping, the invariant is equal to the induced-edge-system's invariant. We also give a new formulation of the...
The possible compatibility of density matrices for single-party subsystems is described by linear constraints on their respective spectra. Whenever some of those quantum marginal constraints are saturated, the total quantum state has a specific, simplified structure. We prove that these remarkable global implications of extremal local information are stable, i.e. they hold approximately for...
We consider entanglement in the three partite system consisting of a qubit, an $m$-level and an $n$-level system. In particular, we use tools introduced in [1] to characterize entanglement transformations under stochastic local operations and classical communication (SLOCC). We find evidence indicating that the following picture is true. In case $m=n$, generic states belong to one of...
Iancu and Mukhopadhyay have proposed a semi-holographic model for heavy-ion collisions, where the saturated hard gluons produced at initial stages are coupled consistently to a holographic theory representing the radiatively emitted strongly coupled soft gluons. The goal is to study thermalization with the ultraviolet (UV) modes described by pQCD and the infrared (IR) modes by gauge/gravity...
The search for heavy Higgs bosons is an important step to probe the parameter space of the minimal supersymmetric Standard Model. We define simplified models for heavy Higgs bosons decaying to supersymmetric particles by using the SModelS framework. We evaluate the viable parameter space by taking into account limits from the Higgs and flavor sector as well as limits from LHC searches for...
We discuss a technique for measuring nonlinear functions of a quantum many-body density matrix, such as Renyi entropies with direct connection to entanglement, without performing full state tomography. Our approach, which has direct connection to Random Matrix Theory, consists in implementing an ensemble of random unitary evolution operators, applying them on the many-body state and extracting...
Quantum Metrology allows one to perform measurements which are quadratically more precise than classically possible. However, the hurdle of implementing the necessary quantum probe states and measurements, whose complexity varies drastically for different metrological scenarios, is usually not taken into account. We show that for a wide range of tasks in metrology, the 2D cluster state can...
We focus on the generation of entanglement among distant parties in a secure way, and with high communication rates.
We show that hashing protocols, a particular class of entanglement purification protocols, enable arbitrary privacy in the presence of noise, even in a setting where the information which noise was applied leaks to the eavesdropper.
As an application thereof we propose a quantum...