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Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: Ashida et al. as discussed by the authors proposed a canonical transformation that completely decouples the impurity from the bath degrees of freedom, and combined this transformation with a Gaussian ansatz for the fermionic bath, obtaining a family of variational many-body states that can efficiently encode the strong entanglement between the impurities and fermions of the bath.
Abstract: We provide a detailed formulation of the recently proposed variational approach [Y. Ashida, T. Shi, M.-C. Ba\~nuls, J. I. Cirac, and E. Demler, Phys. Rev. Lett. 121, 026805 (2018)] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity systems. Motivated by the original ideas of Tomonaga, Lee, Low, and Pines, we construct a canonical transformation that completely decouples the impurity from the bath degrees of freedom. By combining this transformation with a Gaussian ansatz for the fermionic bath, we obtain a family of variational many-body states that can efficiently encode the strong entanglement between the impurity and fermions of the bath. We give a detailed derivation of equations of motions in the imaginary- and real-time evolutions on the variational manifold. We benchmark our approach by applying it to investigate ground-state and dynamical properties of the anisotropic Kondo model and compare results with those obtained using the matrix-product state (MPS) ansatz. We show that our approach can achieve an accuracy comparable to MPS-based methods with several orders of magnitude fewer variational parameters than the corresponding MPS ansatz. Comparisons to the Yosida ansatz and the exact solution from the Bethe ansatz are also discussed. We use our approach to investigate the two-lead Kondo model and analyze its long-time spatiotemporal behavior and the conductance behavior at finite bias and magnetic fields. The obtained results are consistent with the previous findings in the Anderson model and the exact solutions at the Toulouse point.
35 citations
TL;DR: The problem of equivalence under coordinate changes and output transformations to observer canonical forms is addressed in discrete time for multi-output systems and yields a straightforward observer design with linear error dynamics.
35 citations
TL;DR: In this paper, a new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided, which allows us to give a natural description of dressing transformations, string equations and additional symmetries.
Abstract: A new description of the universal Whitham hierarchy in terms of a factorization problem in the Lie group of canonical transformations is provided. This scheme allows us to give a natural description of dressing transformations, string equations and additional symmetries for the Whitham hierarchy. We show how to dress any given solution and prove that any solution of the hierarchy may be undressed, and therefore comes from a factorization of a canonical transformation. A particularly important function, related to the tau-function, appears as a potential of the hierarchy. We introduce a class of string equations which extends and contains previous classes of string equations considered by Krichever and by Takasaki and Takebe. The scheme is also applied for a convenient derivation of additional symmetries. Moreover, new functional symmetries of the Zakharov extension of the Bentley gas equations are given and the action of additional symmetries over the potential in terms of linear PDEs is characterized.
35 citations
TL;DR: A general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem is presented, which approaches such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart.
Abstract: We present a general theoretical framework for a hybrid system that is composed of a quantum subsystem and a classical subsystem. We approach such a system with a simple canonical transformation which is particularly effective when the quantum subsystem is dynamically much faster than the classical counterpart, which is commonly the case in hybrid systems. Moreover, this canonical transformation generates a vector potential which, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics and, on the other hand, yields a Lorentz-like geometric force in the slow classical dynamics.
35 citations
TL;DR: Approximate signal reconstruction formulas for theclass of L 2(R) signals in the fractional Fourier and linear canonical transform (LCT) domains are presented and provide exact representation for the class of signals that can be expressed in the form of polynomials of some finite order.
Abstract: Approximate signal reconstruction formulas for the class of L 2(R) signals in the fractional Fourier and linear canonical transform (LCT) domains are presented. The results make use of the finite number of nonuniform samples of the signal in fractional Fourier or LCT domains taken at the positions determined by the zeros of the Hermite polynomials. The results provide exact representation for the class of signals that can be expressed in the form of polynomials of some finite order. The truncation error bounds in the presented results are also discussed. Simulation results for some of the proposed theorems are also presented.
34 citations