Search results for "Tonian"
showing 10 items of 802 documents
Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
2011
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.
Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields
2017
The quantum dynamics of a $\hat{\mathbf{J}}^2=(\hat{\mathbf{j}}_1+\hat{\mathbf{j}}_2)^2$-conserving Hamiltonian model describing two coupled spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of $\hat{\mathbf{J}}^2$ is dynamically invariant and the Hamiltonian of the total system restricted to any one of such $(j_1+j_2)-|j_1-j_2|+1$ eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical…
Quench of symmetry broken ground states
2016
We analyze the problem of how different ground states associated to the same set of the Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained projecting two ground states in the same subset. Before the quench, regardless the particular choice of the subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum of the distinguishability shows an exponential deca…
Emergent hydrodynamics in a strongly interacting dipolar spin ensemble.
2021
Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific challenge. In particular, it is difficult to quantitatively predict the emergent "classical" properties of a system (e.g. diffusivity, viscosity, compressibility) from a generic microscopic quantum Hamiltonian. Here, we introduce a hybrid solid-state spin platform, where the underlying disordered, dipolar quantum Hamiltonian gives rise to the emergence of unconventional spin diffusion at nanometer length scales. In particular, the combination of positional di…
Topological Signatures in the Electronic Structure of Graphene Spirals
2013
Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to tim…
Consistent probabilistic description of the neutral Kaon system
2013
The neutral Kaon system has both CF violation in the mass matrix and a non-vanishing lifetime difference in the width matrix. This leads to an effective Hamiltonian which is not a normal operator, with incompatible (non-commuting) masses and widths. In the Weisskopf-Wigner Approach (WWA), by diagonalizing the entire Hamiltonian, the unphysical non-orthogonal "stationary" states K-L,K-S are obtained. These states have complex eigenvalues whose real (imaginary) part does not coincide with the eigenvalues of the mass (width). matrix. In this work we describe the system as an open Lindblad-type quantum mechanical system due to Kaon decays. This approach, in terms of density matrices for initial…
Measurement-induced optical Kerr interaction
2013
We present a method for implementing a weak optical Kerr interaction (single-mode Kerr Hamiltonian) in a measurement-based fashion using the common set of universal elementary interactions for continuous-variable quantum computation. Our scheme is a conceptually distinct alternative to the use of naturally occurring, weak Kerr nonlinearities or specially designed nonlinear media. Instead, we propose to exploit suitable offline prepared quartic ancilla states together with beam splitters, squeezers, and homodyne detectors. For perfect ancilla states and ideal operations, our decompositions for obtaining the measurement-based Kerr Hamiltonian lead to a realization with near-unit fidelity. Non…
Effective Landau-Zener transitions in circuit dynamical Casimir effect with time-varying modulation frequency
2016
We consider the dissipative single-qubit circuit QED architecture in which the atomic transition frequency undergoes a weak external time-modulation. For sinusoidal modulation with linearly varying frequency we derive effective Hamiltonians that resemble the Landau-Zener problem of finite duration associated to a two- or multi-level systems. The corresponding off-diagonal coupling coefficients originate either from the rotating or the counter-rotating terms in the Rabi Hamiltonian, depending on the values of the modulation frequency. It is demonstrated that in the dissipation less case one can accomplish almost complete transitions between the eigenstates of the bare Rabi Hamiltonian even f…
Pseudo-fermions in an electronic loss-gain circuit
2013
In some recent papers a loss-gain electronic circuit has been introduced and analyzed within the context of PT-quantum mechanics. In this paper we show that this circuit can be analyzed using the formalism of the so-called pseudo-fermions. In particular we discuss the time behavior of the circuit, and we construct two biorthogonal bases associated to the Liouville matrix $\Lc$ used in the treatment of the dynamics. We relate these bases to $\Lc$ and $\Lc^\dagger$, and we also show that a self-adjoint Liouville-like operator could be introduced in the game. Finally, we describe the time evolution of the circuit in an {\em Heisenberg-like} representation, driven by a non self-adjoint hamilton…
Interaction-free evolving states of a bipartite system
2014
We show that two interacting physical systems may admit entangled pure or non separable mixed states evolving in time as if the mutual interaction hamiltonian were absent. In this paper we define these states Interaction Free Evolving (IFE) states and characterize their existence for a generic binary system described by a time independent Hamiltonian. A comparison between IFE subspace and the decoherence free subspace is reported. The set of all pure IFE states is explicitly constructed for a non homogeneous spin star system model.