715 research outputs found
Nonlinear dynamics and quantum chaos: an introduction
No full textThe field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field
Nonlinear Dynamics and Quantum Chaos: An Introduction
No full textThis book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field
Many Body Quantum Chaos
No full textThis editorial remembers Shmuel Fishman, one of the founding fathers of the research field "quantum chaos", and puts into context his contributions to the scientific community with respect to the twelve papers that form the special issue
Hybrid quantum systems - New perspectives on quantum state control
No full textWe give a brief sketch of the emerging field of quantum mechanical hybrid systems through a cross section of research papers on topics of current interest contained in this Topical Issue
Dynamik ultrakalter Quantengase
No full textModern quantum and atom-optical experiments allow for an unprecedented control
of microscopic degrees of freedom, not just in the initialization but also
in the dynamical evolution of quantum states. This talk focuses on the dynamics
of ultracold bosons in optical lattice structures. As a paradigm, we report on
experimental as well as theoretical results on the interband transport in a
tilted lattice, i.e., a realization of the famous Wannier-Stark problem. An
extended Bose-Hubbard model is presented for two coupled energy bands. For
reasonable lattice sizes, this model gives access to the full quantum
spectrum, which allows us a good characterization of ``horizontal''
(spatially) and ``vertical'' (energetic) quantum transport. For specific
parameters, resonant tunnelling between the bands can be exploited to map the
original model onto a much simpler effective spin Hamiltonian. We conclude with general perspectives on future directions of our study of strongly correlated bosons in lattice structures
Models for a multimode bosonic tunneling junction
No full textWe discuss the relaxation dynamics for a bosonic tunneling junction with two modes in the central potential well. We use a master equation description for ultracold bosons tunneling in the presence of noise and incoherent coupling processes into the two central modes. Whilst we cannot quantitatively reproduce the experimental data of the setup reported in [Phys. Rev. Lett. 115, 050601 (2015)], we find a reasonable qualitative agreement of the refilling process of the initially depleted central site. Our results may pave the way for the control of bosonic tunneling junctions by the simultaneous presence of decoherence processes and atom-atom interaction
Die wunderbare Welt der ultrakalten Atome
No full textChaos und Unordnung bedeuten in unserem Alltagsleben üblicherweise nichts Gutes. Schon die antike griechische Mythologie belegte den Begriff „Chaos“ mit negativen Assoziationen, ein ungeordneter Zustand, eine unklare „Ursuppe“, die erst durch Regeln und das Einführen einer göttlichen Ordnung zum „Kosmos“, also zu unserem Universum, wurde
Applications of fidelity measures to complex quantum systems
No full textWe revisit fidelity as a measure for the stability and the complexity of the quantum motion of singleand many-body systems. Within the context of cold atoms, we present an overview of applications of two fidelities, which we call static and dynamical fidelity, respectively. The static fidelity applies to quantum problems which can be diagonalized since it is defined via the eigenfunctions. In particular, we show that the static fidelity is a highly effective practical detector of avoided crossings characterizing the complexity of the systems and their evolutions. The dynamical fidelity is defined via the time-dependent wave functions. Focusing on the quantum kicked rotor system, we highlight a few practical applications of fidelity measurements in order to better understand the large variety of dynamical regimes of this paradigm of a low-dimensional system with mixed regular-chaotic phase space
Spontaneous emission in quantum walks of a kicked Bose-Einstein condensate
No full textWe analytically investigate the recently proposed and implemented discrete-time quantum walk based on a kicked Bose-Einstein condensate. We extend previous work on the effective dynamics by taking into account spontaneous emission due to the kicking light. Spontaneous emission affects both the internal and external degrees of freedom arising from the entanglement between them during the walk dynamics. The result is a measurable degradation of the experimental walk signal that we characterize
Quantum walk of a Bose-Einstein condensate in the Brillouin zone
No full textWe propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow for a robust implementation of quantum walks with several tens of steps at least. In addition, on-site atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone
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