Related papers: Notes on Some Questions in Mathematical Physics an…
In this work we examine the effect of phase-space noncommutativity on some typically quantum properties such as quantum beating, quantum information, and decoherence. To exemplify these issues we consider the two-dimensional noncommutative…
Classical and quantum correlation functions are derived for a system of non-interacting particles moving on a circle. It is shown that the decaying behaviour of the classical expression for the correlation function can be recovered from the…
A one-dimensional quantum wire of Fermions is considered and ground state properties are calculated in the high density regime within the extended quasiparticle picture and Born approximation. Expanding the two-particle Green functions…
We analyze the role of resonances in two-fermion entanglement production for a quasi one-dimensional two channel scattering problem. We solve exactly for the problem of a two-fermion antisymmetric product state scattering off a double delta…
Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and Master equation. Combination of this analysis with recent experiments on the magnetoconductance allows for the first time…
We prove spatial decay estimates on disorder-averaged position-momentum correlations in a gapless class of random oscillator models. First, we prove a decay estimate on dynamic correlations for general eigenstates with a bound that depends…
Recent work has examined how undecidable problems can arise in quantum information science. We augment this by introducing three new undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the…
We study the ground state properties of the one-dimensional extended Hubbard model at half-filling from the perspective of its particle reduced density matrix. We focus on the reduced density matrix of $2$ fermions and perform an analysis…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
By using the so-called matrix-product ground state approach, a few one-dimensional quantum systems, including a frustrated spin-1/2 Heisenberg ladder, the ferromagnetic t-J-V model at half-filling, the antiferromagnetic $J_z-V$ at 2/3…
In this paper we give a self contained introduction to the conceptional and mathematical foundations of quantum information theory. In the first part we introduce the basic notions like entanglement, channels, teleportation etc. and their…
Area laws for entanglement in quantum many-body systems give useful information about their low-temperature behaviour and are tightly connected to the possibility of good numerical simulations. An intuition from quantum many-body physics…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
We present a description of finite dimensional quantum entanglement, based on a study of the space of all convex decompositions of a given density matrix. On this space we construct a system of real polynomial equations describing separable…
The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present new tools for learning about…
While exponential decay is ubiquitous in Nature, deviations at both short and long times are dictated by quantum mechanics. Non-exponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying…
In this paper, we shed light on relations between three concepts studied in representations theory, algebraic geometry and quantum information theory. First - spherical actions of reductive groups on projective spaces. Second - secant…
Quantum dots are nanometer-scale semiconductor particles that exhibit size-dependent quantum mechanical properties. In this work, we investigate the dynamics of quantum correlations, quantified by the concurrence and the quantum coherence,…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…
Contact has been well established as an important quantity to govern dilute quantum systems, in which the pairwise correlation at short distance traces a broad range of thermodynamic properties. So far, studies have been focusing on contact…