相关论文: Semiclassical Symmetries
We consider the semiclassical ballistic sigma-model as an effective theory describing the quantum mechanics of classically chaotic systems. Specifically, we elaborate on close analogies to the recently developed semiclassical theory of…
For nonrelativistic Hamiltonians which are shape invariant, analytic expressions for the eigenvalues and eigenvectors can be derived using the well known method of supersymmetric quantum mechanics. Most of these Hamiltonians also possess…
A formalism describing the dynamics of classical and quantum systems from a group theoretical point of view is presented. We apply it to the simple example of the classical free particle. The Galileo group $G$ is the symmetry group of the…
Quantum mechanics exhibits a wide range of nonclassical features, of which entanglement in multipartite systems takes a central place. In several specific settings, it is well known that nonclassicality (e.g., squeezing, spin squeezing,…
A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
Various kinds of infinitary operations satisfying forms of associativity have been considered in the literature by various authors, including A. Tarski, C. Karp, J. H. Conway, D. Krob, N. Bedon, and C. Rispal. Applications include the…
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…
The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the…
Symmetry underlies many of the most effective classical and quantum learning algorithms, yet whether quantum learners can gain a fundamental advantage under symmetry-imposed structures remains an open question. Based on evidence that…
Conservation of symmetries plays a crucial role in both classical and quantum simulations of many-body systems, enabling the tracking of states with specific symmetry properties and leading to substantial reductions in the number of…
Semi-classical states in homogeneous loop quantum cosmology (LQC) are constructed by two different ways. In the first approach, we firstly construct an exponentiated annihilation operator. Then a kind of semi-classical (coherent) state is…
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
I discuss a set of strong, but probabilistically intelligible, axioms from which one can {\em almost} derive the appratus of finite dimensional quantum theory. Stated informally, these require that systems appear completely classical as…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We derive a "classical-quantum" approximation scheme for a broad class of bipartite quantum systems from fully quantum dynamics. In this approximation, one subsystem evolves via classical equations of motion with quantum corrections, and…