The Center of Small Quantum Groups I: The Principal Block in Type A

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We classify the spherical birational sheets in a complex simple simply-connected algebraic group. We use the classification to show that, when G is a connected reductive complex algebraic group with simply-connected derived subgroup, two conjugacy classes ...

Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been developed. Howe ...

Quantum computing holds the promise to solve many of today's intractable problems. A solid-state quantum computer (QC) is generally made of an array of qubits implemented in one of many solid-state technologies and operating at deep-cryogenic temperatures ...

We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and φ : G → GL(V ) is a non-trivial irreducible repres ...

Quantum computers are invaluable tools to explore the properties of complex quantum systems. We show that dynamical localization of the quantum sawtooth map, a highly sensitive quantum coherent phenomenon, can be simulated on actual, small-scale quantum pr ...

The seminal work of DiPerna and Lions (Invent Math 98(3):511-547, 1989) guarantees the existence and uniqueness of regular Lagrangian flows for Sobolev vector fields. The latter is a suitable selection of trajectories of the related ODE satisfying addition ...

The complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum m ...

Let G be a simply connected simple algebraic group over an al- gebraically closed ﬁeld k of characteristic p > 0. The category of rationalG-modules is not semisimple. We consider the question of when the tensorproduct of two simple G-modules L(λ) and L(μ) ...

We show that the imaginary multiplicative chaos exp(i beta Gamma) determines the gradient of the underlying field Gamma for all log-correlated Gaussian fields with covariance of the form -log|x-y|+g(x,y) with mild regularity conditions on g, for all d >= 2 ...

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

Recently, SU(3) chains in the symmetric and self-conjugate representations have been studied using field theory techniques. For certain representations, namely rank-psymmetric ones with pnot a multiple of 3, it was argued that the ground state exhibits gap ...

Methods of topological data analysis have been successfully applied in a wide range of fields to provide useful summaries of the structure of complex data sets in terms of topological descriptors, such as persistence diagrams. While there are many powerful ...

With the development of quantum optics, photon correlations acquired a prominent role as a tool to test our understanding of physics, and played a key role in verifying the validity of quantum mechanics. The spatial and temporal correlations in a light fie ...

We study correlation functions involving generalized ANEC operators of the form integral dx-x-n+2T--x -> in four dimensions. We compute two, three, and ...

The hemocyanin protein binds and transports molecular oxygen via two copper atoms at its core. The singlet state of the Cu2O2 core is thought to be stabilised by a superexchange pathway, but detailed in situ computational analysis is complicated by the mul ...

The Center of Small Quantum Groups I: The Principal Block in Type A

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Spherical birational sheets in reductive groups

A quantum algorithm for the direct estimation of the steady state of open quantum systems

A Fully-Integrated 40-nm 5-6.5 GHz Cryo-CMOS System-on-Chip with I/Q Receiver and Frequency Synthesizer for Scalable Multiplexed Readout of Quantum Dots

Spectra of non-regular elements in irreducible representations of simple algebraic groups

Dynamical Localization Simulated on Actual Quantum Hardware

Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

Variational Monte Carlo Calculations of A

On complete reducibility of tensor products of simple modules over simple algebraic groups

Reconstructing the base field from imaginary multiplicative chaos

On arithmetic progressions in symmetric sets in finite field model

Optimal radial basis for density-based atomic representations

Generalization of the Haldane conjecture to SU(n) chains

From Trees to Barcodes and Back Again: Theoretical and Statistical Perspectives

Non-classical photon-phonon correlations at room temperature

On the stress tensor light-ray operator algebra

Superexchange mechanism and quantum many body excitations in the archetypal di-Cu oxo-bridge