The vector potential and Berry-phase-induced force in a dissipative hybrid system are studied in this paper. The hybrid system is a compound of a classical magnetic particle and a quantum single spin. Two cases are considered. In the first case, we investigate the effect of the dissipative quantum subsystem on the motion of its classical partner, whereas in the second case, we show how the dynamics of the quantum single spin are affected by the dissipation of the classical particle. Extension to general dissipative hybrid systems is discussed.
The vector potential and Berry-phase-induced force in a dissipative hybrid system are studied in this paper. The hybrid system is a compound of a classical magnetic particle and a quantum single spin. Two cases are considered. In the first case, we investigate the effect of the dissipative quantum subsystem on the motion of its classical partner, whereas in the second case, we show how the dynamics of the quantum single spin are affected by the dissipation of the classical particle. Extension to general dissipative hybrid systems is discussed.
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.
It is well known that the dynamics of a hybrid system, which consists of a quantum subsystem and a classical subsystem, can be studied by transforming the quantum subsystem into a classical one. Based on our previous work [Phys. Rev. A 102, 032213 (2020)], we present the formalism of the quantum-classical hybrid system containing a quantum subsystem with energy degeneracy. By simulating the non-Abelian dynamics and geometric phases for the quantum subsystem with classical non-Abelian dynamics and geometric angles, the effect of the non-Abelian gauge field and the geometric phase of the quantum (sub)system on the dynamics of the classical subsystem is revealed by a simple canonical transformation. Remarkably, the non-Abelian angle geometric vector potential is found not only to induce the Wilczek-Zee phase in the dynamics of the quantum subsystem but also to give rise to a Lorentz-like non-Abelian geometric force. To illustrate the dynamics of the hybrid system, we examine the interaction between a spin-half particle and a magnetic field coupled with a magnetic particle. The explicit expression of the non-Abelian magneticlike gauge field is presented, introducing a different form of non-Abelian geometric force in the realm of quantum-classical dynamics.
Due to the potential application in quantum information process, geometric phase of interacting system arouse many interests. Some physicists concentrate on the system in pure classical envi- ronment, while others study the system in pure quantized environment. So a natural question is asked: how about an interacting system in composite environments made up of both classical and quantized field. In this letter, we analyze a quantum system composed of two interacting spins, of which one is in classical magnetic field and the other is in quantized field. First, classical magnetic field driven Berry phases for the whole system and subsystem are studied. The effect of couplings between particles and photon on these phases are analyzed. In comparison with the dynamical quantized field, We find that even a static quantized field in its vacuum state can also have an effect on Berry phase. Second, quantized field driven Berry phases for the whole system and sub- system are formulated, including both one and two mode of this field. The vacuum induced effects are elaborated, moreover compared with the constant vacuum induced phases in former papers, the counterpart in this letter varies according to classical magnetic field, couplings and other pa- rameters. For the two mode quantized field, the rigorous relationship between the concurrence and Berry phase for subsystem are built up.
We calculate Berry’s phase when the driving field, to which a spin-[Formula: see text] is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in general, components, e.g. the angular momentum of another particle, or another spin. The geometric phase of the entire system, spin plus “quantum driving field”, is first computed, and is then subdivided into the two subsystems, using the Schmidt decomposition of the total wave function — the resulting expression shows a marked, purely quantum effect, involving the commutator of the field components. We also compute the corresponding mean “classical” phase, involving a precessing magnetic field in the presence of noise, up to terms quadratic in the noise amplitude — the results are shown to be in excellent agreement with numerical simulations in the literature. Subtleties in the relation between the quantum and classical case are pointed out, while three concrete examples illustrate the scope and internal consistency of our treatment.
In this paper, we study the effect of quantum subsystem–subsystem coupling on the magnetic-like field that the classical subsystem feels in a quantum–classical hybrid system. The hybrid system is composed of a classical magnetic particle and two coupled spins. We show that (i) when the spin–spin interaction is equal to the magnetic–spin interaction, the magnetic-like field changes sharply. This observation becomes more clear when the distance between the two subsystems is much longer than the magnetic particle's rotating radius. (ii) When the spin–spin interaction is larger than the coupling between the quantum classical systems, the effect that the quantum subsystem acts on in the classical part approaches zero. Some useful applications are also discussed.
We discuss the concept of the Berry phase in a dissipative system. We show that one can identify a Berry phase in a weakly-dissipative system and find the respective correction to this quantity, induced by the environment. This correction is expressed in terms of the symmetrized noise power and is therefore insensitive to the nature of the noise representing the environment, namely whether it is classical or quantum mechanical. It is only the spectrum of the noise which counts. We analyze a model of a spin-half (qubit) anisotropically coupled to its environment and explicitly show the coincidence between the effect of a quantum environment and a classical one.