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Register a new userQuantifying Algebraic Asymmetry of Hamiltonian Systems
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The symmetries play important roles in physical systems. We study the symmetries of a Hamiltonian system by investigating the asymmetry of the Hamiltonian with respect to certain algebras. We define the asymmetry of an operator with respect to an algebraic basis in terms of their commutators. Detailed analysis is given to the Lie algebra $mathfrak{su}(2)$ and its $q$-deformation. The asymmetry of the $q$-deformed integrable spin chain models is calculated. The corresponding geometrical pictures with respect to such asymmetry is presented.
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We discuss the alternative algebraic structures on the manifold of quantum states arising from alternative Hermitian structures associated with quantum bi-Hamiltonian systems. We also consider the consequences at the level of the Heisenberg picture in terms of deformations of the associative product on the space of observables.
The possibility of a quantum system to exhibit properties that are akin to both the classically held notions of being a particle and a wave, is one of the most intriguing aspects of the quantum description of nature. These aspects have been instrumental in understanding paradigmatic natural phenomena as well as to provide nonclassical applications. A conceptual foundation for the wave nature of a quantum state has recently been presented, through the notion of quantum coherence. We introduce here a parallel notion for the particle nature of a quantum state of an arbitrary physical system. We provide elements of a resource theory of particleness, and give a quantification of the same. Finally, we provide evidence for a complementarity between the particleness thus introduced, and the coherence of an arbitrary quantum state.
We study the quantification of coherence in infinite dimensional systems, especially the infinite dimensional bosonic systems in Fock space. We show that given the energy constraints, the relative entropy of coherence serves as a well-defined quantification of coherence in infinite dimensional systems. Via using the relative entropy of coherence, we also generalize the problem to multi-mode Fock space and special examples are considered. It is shown that with a finite average particle number, increasing the number of modes of light can enhance the relative entropy of coherence. With the mean energy constraint, our results can also be extended to other infinite-dimensional systems.
We propose a `Floquet engineering formalism to systematically design a periodic driving protocol in order to stroboscopically realize the desired system starting from a given static Hamiltonian. The formalism is applicable to quantum systems which have an underlying closed Lie-algebraic structure, for example, solid-state systems with noninteracting particles moving on a lattice or its variant described by the ultra-cold atoms moving on an optical lattice. Unlike previous attempts at Floquet engineering, our method produces the desired Floquet Hamiltonian at any driving frequency and is not restricted to the fast or slow driving regimes. The approach is based on Wei-Norman ansatz, which was originally proposed to construct a time-evolution operator for any arbitrary driving. Here, we apply this ansatz to the micro-motion dynamics, defined within one period of the driving, and obtain the driving protocol by fixing the gauge of the micro-motion. To illustrate our idea, we use a two-band system or the systems consisting of two sub-lattices as a testbed. Particularly, we focus on engineering the cross-stitched lattice model that has been a paradigmatic flat-band model.
Here we deal in a pedagogical way with an approach to construct an algebraic structure for the Quantum Mechanical measurement processes from the concept of emph{Measurement Symbol}. Such concept was conceived by Julian S. Schwinger and constitutes a fundamental piece in his variational formalism and its several applications.
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