相关论文: Base-controlled mechanical systems and geometric p…

We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…

The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion for three singular systems are obtained as total differential equations in many variables. The integrability conditions for these syatems lead us to the…

The article concerns the geometrical theory of general systems $\Omega$ of partial differential equations in the \emph{absolute sense}, i.e., without any additional structure and subject to arbitrary change of variables in the widest…

We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…

It is proposed that the mathematical models for any physical systems that are based in first principles, such as conservation laws or balance principles, have some common elements, namely, a space of kinematical states, a space of dynamical…

We present a detailed discussion of a general theory of phase-space distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9 (1998)]. This theory provides a unified phase-space formulation of quantum mechanics for physical…

Geometric phases have been shown to be feasible in implementing quantum gates to perform quantum information processing. For all the realistic applications, the environmental influence on the geometric phase and decoherence such as memory…

Legged robots are typically in rigid contact with the environment at multiple locations, which add a degree of complexity to their control. We present a method to control the motion and a subset of the contact forces of a floating-base…

We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and…

Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and…

We present a novel geometric approach for determining the unique structure of a Hamiltonian and establishing an instability criterion for quantum quadratic systems. Our geometric criterion provides insights into the underlying geometric…

The constraint operators belonging to a generally covariant system are found out within the framework of the BRST formalism. The result embraces quadratic Hamiltonian constraints whose potential can be factorized as a never null function…

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables - inaccessible conceptually derived variables; several examples of such variables are given. The focus is…

Mechanistic interpretability has transformed the analysis of transformer circuits by decomposing model behavior into competing algorithms, identifying phase transitions during training, and deriving closed-form predictions for when and why…

Composite system is studied in noncommutative phase space with preserved rotational symmetry. We find conditions on the parameters of noncommutativity on which commutation relations for coordinates and momenta of the center-of-mass of…

The geometric phase induced in an auxiliary qubit by a many-body system is calculated and discussed. Two kinds of coupling between the auxiliary qubit and the many-body system are considered, which lead to dephasing and dissipation in the…

Following a brief historical introduction of the notions of chaos in dynamical systems, we will present recent developments that attempt to profit from the rich structure and complexity of the chaotic dynamics. In particular, we will…

In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…

As is well known, an external magnetic field in configuration space coupled to a quantum dynamics induces noncommutativity in its velocity momentum space. By phase space duality, an external vector potential in the conjugate momentum sector…

It is shown how to exactly simulate many-body interactions and multi-qubit gates by coupling finite dimensional systems, e.g., qubits with a continuous variable. Cyclic evolution in the phase space of such a variable gives rise to a…