On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in Two Dimensions
2012
Abstract: We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum dot -- the maximal number of electrons does not exceed twice the nuclear charge. It result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of |\bx| T(\bp) + T(\bp) |\bx| which -- in two dimensions -- is false for the non-relativistic case T(\bp) = \bp^2, but is proven in this paper for T(\bp) = |\bp|, i.e., the ultra-relativistic kinetic energy. |
Scaling of the thermal spectral function for quantum critical bosons in one dimension
2012
Abstract: We present an improved scheme for the precise evaluation of finite-temperature response functions of strongly correlated systems in the framework of the time-dependent density matrix renormalization group. The maximum times that we can reach at finite temperatures T are typically increased by a factor of two, when compared against the earlier approaches. This novel scheme, complemented with linear prediction, allows us now to evaluate dynamic correlators for interacting bosons in one dimension. We demonstrate that the considered spectral function in the quantum critical regime with dynamic critical exponent z=2 is captured by the universal scaling form S(k,omega)=(1/T)*Phi(k/sqrt(T),omega/T) and calculate the scaling function precisely. |
Nuclear spin physics in quantum dots: an optical investigation
Reviews of Modern Physics
, Volume 85,, page: 79
2012
Abstract: The mesoscopic spin system formed by the 10E4-10E6 nuclear spins in a semiconductor quantum dot offers a unique setting for the study of many-body spin physics in the condensed matter. The dynamics of this system and its coupling to electron spins is fundamentally different from its bulk counter-part as well as that of atoms due to increased fluctuations that result from reduced dimensions. In recent years, the interest in studying quantum dot nuclear spin systems and their coupling to confined electron spins has been fueled by its direct implication for possible applications of such systems in quantum information processing as well as by the fascinating nonlinear (quantum-)dynamics of the coupled electron-nuclear spin system. In this article, we review experimental work performed over the last decades in studying this mesoscopic,coupled electron-nuclear spin system and discuss how optical addressing of electron spins can be exploited to manipulate and read-out quantum dot nuclei. We discuss how such techniques have been applied in quantum dots to efficiently establish a non-zero mean nuclear spin polarization and, most recently, were used to reduce fluctuations of the average quantum dot nuclear spin orientation. Both results in turn have important implications for the preservation of electron spin coherence in quantum dots, which we discuss. We conclude by speculating how this recently gained understanding of the quantum dot nuclear spin system could in the future enable experimental observation of quantum-mechanical signatures or possible collective behavior of mesoscopic nuclear spin ensembles. |
Real analyticity away from the nucleus of pseudorelativistic Hartree-Fock orbitals
Analysis & PDE
, Volume 5, page: ,no.3,657--691
2011
Abstract: We prove that the Hartree--Fock orbitals of pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator sqrt-Delta+1-1, are real analytic away from the origin. As a consequence, the quantum mechanical ground state of such atoms is never a Hartree-Fock state. Our proof is inspired by the classical proof of analyticity by nested balls of Morrey and Nirenberg. However, the technique has to be adapted to take care of the non-local pseudodifferential operator, the singularity of the potential at the origin, and the non-linear terms in the equation. |
Quasi-locality and efficient simulation of Markovian quantum dynamics
Phys. Rev. Lett.
, Volume 108,, page: 230504
2011
Abstract: We consider open many-body systems governed by a time-dependent quantum master equation with short-range interactions. With a generalized Lieb-Robinson bound, we show that the evolution in this very generic framework is quasi-local, i.e., the evolution of observables can be approximated by implementing the dynamics only in a vicinity of the observables' support. The precision increases exponentially with the diameter of the considered subsystem. Hence, the time-evolution can be simulated on classical computers with a cost that is independent of the system size. Providing error bounds for Trotter decompositions, we conclude that the simulation on a quantum computer is additionally efficient in time. For experiments and simulations, our result can be used to rigorously bound finite-size effects. |
Spectral functions in one-dimensional quantum systems at T>0
Phys. Rev. B
, Volume 79,, page: 245101
2009
Abstract: We present for the first time time-dependent density-matrix renormalization-group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics, for arbitrary temperatures. This is illustrated with spin structure factors of XX and XXX spin-1/2 chains. For the XX model we can compare against an exact solution and for the XXX model (Heisenberg antiferromagnet) against a Bethe Ansatz solution and quantum Monte Carlo data. |
Many-Body Physics with Ultracold Gases
Rev. Mod. Phys.
, Volume 80,, page: 885
2007
Abstract: This article reviews recent experimental and theoretical progress on many-body phenomena in dilute, ultracold gases. Its focus are effects beyond standard weak-coupling descriptions, like the Mott-Hubbard-transition in optical lattices, strongly interacting gases in one and two dimensions or lowest Landau level physics in quasi two-dimensional gases in fast rotation. Strong correlations in fermionic gases are discussed in optical lattices or near Feshbach resonances in the BCS-BEC crossover. |
Physicists create quantum system, which is robust to mixing by periodic forces
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