相关论文: Geometry of quantum dynamics and a time-energy unc…

Riemannian metric on real 2n-dimensional space associated with the equation governing complex diffusion of pure states of an open quantum system is introduced and studied. Examples of a qubit under the influence of dephasing and thermal…

We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to…

We consider quantum systems with energy constraints relative to a reference Hamiltonian. In general, quantum channels and continuous-time dynamics need not satisfy energy conservation. Physically meaningful channels, however, only introduce…

The minimal time required for a system to evolve between two different states is an important notion for developing ultra-speed quantum computer and communication channel. Here, we introduce a new metric for non-degenerate density operator…

We establish the minimum time it takes for an initial state of mean energy E and energy spread DE to move from its initial configuration by a predetermined amount. Distances in Hilbert space are estimated by the fidelity between the initial…

We present a simple proof of the minimum time for the quantum evolution between two arbitrary states. This proof is performed in the absence of any geometrical arguments. Then, being in the geometric framework of quantum evolutions based…

In this thesis we provide a uniform treatment of two non-adiabatic geometric phases for dynamical systems of mixed quantum states, namely those of Uhlmann and of Sj\"{o}qvist et al. We develop a holonomy theory for the latter which we also…

The mixed density operator for coarsegrained eigenlevels of a static Hamiltonian is represented in phase space by the spectral Wigner function, which has its peak on the corresponding classical energy shell. The action of trajectory…

While a pure quantum state may accumulate both the Berry phase and dynamic phase as it undergoes a cyclic path in the parameter space, the situation is more complicated when mixed quantum states are considered. From the Ulhmann bundle, a…

Quantum coherence, rooted in the superposition principle of quantum mechanics, is a crucial quantum resource. Various measures, operational interpretations, and generalizations of quantum coherence have been proposed. In recent years, its…

The study of quantum systems evolving from initial states to distinguishable, orthogonal final states is important for information processing applications such as quantum computing and quantum metrology. However, for most unitary evolutions…

In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in…

Both conservation laws and practical restrictions impose symmetry constraints on the dynamics of open quantum systems. In the case of time-translation symmetry, which arises naturally in many physically relevant scenarios, the quantum…

Quantum particles under geometric constraints are sensitive to the geometry and topology of the underlying space. We analytically study the laser-driven nonlinear dynamics of a quantum particle whose motion is constrained to a…

In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $\phi(k,E)$ is…

We use geometric concepts originally proposed by Anandan and Aharonov to show that the Farhi-Gutmann time optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical…

The eigenvalue of the hermitic Hamiltonian is real undoubtedly. Actually, The reality can also be guaranteed by the $PT$-symmetry. The hermiticity and the $PT$-symmetric quantum theory both have requirements regarding the boundary…

The unitary dynamics of quantum systems can be modeled as a trajectory on a Riemannian manifold. This theoretical framework naturally yields a purely geometric interpretation of computational complexity for quantum algorithms, a notion…

We present the time dynamics of twisted quantum states. We find an explicit connection between the well-known stationary Landau state and an evolving twisted state, even when the Hamiltonian accounts for linear energy dissipation. Utilizing…