Related papers: Quantum toboggans with two branch points

Spin networks, essentially labeled graphs, are ``good quantum numbers'' for the quantum theory of geometry. These structures encompass a diverse range of techniques which may be used in the quantum mechanics of finite dimensional systems,…

For quantum (quasi)particles living on complex toboggan-shaped curves which spread over N Riemann sheets the approximate evaluation of topology-controlled bound-state energies is shown feasible. In a cubic-oscillator model the low-lying…

Superfluid turbulence, often referred to as quantum turbulence, is a fascinating phenomenon for which a satisfactory theoretical framework is lacking. Holographic duality provides a systematic new approach to studying quantum turbulence by…

A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…

Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…

This paper presents a new approach to phase space trajectories in quantum mechanics. A Moyal description of quantum theory is used, where observables and states are treated as classical functions on a classical phase space. A quantum…

For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial…

We show how conformal invariance predicts the functional form of two-point correlators in one-dimensional periodic quantum systems. Numerical evidence for this functional form in a wide class of models --- including long-ranged ones --- is…

Machine learning has been applied on a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems for the identification of phase transitions. The recently proposed quantum convolutional neural…

We introduce a geometric path integral definition of wormhole partition functions in a general class of 1D quantum systems obtained by quantizing a phase space. We compute the wormhole partition function in a semi-classical limit and in…

Neural network-based algorithms have garnered considerable attention in condensed matter physics for their ability to learn complex patterns from very high dimensional data sets towards classifying complex long-range patterns of…

We show that dynamical quantum phase transitions (DQPTs) in the quench dynamics of two-dimensional topological systems can be characterized by a dynamical topological invariant defined along an appropriately chosen closed contour in…

Complicated time-dependent curved spacetime and electric field are involved in many astrophysical situations, including the early universe, Hawking radiation, the Schwinger effect, and gravitational pair production. In this Letter, a…

Certain fractional quantum Hall wavefunctions -- particularly including the Laughlin, Moore-Read, and Read-Rezayi wavefunctions -- have special structure that makes them amenable to analysis using an exeptionally wide range of techniques…

Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…

The current work addresses quantum machine learning in the context of Quantum Artificial Neural Networks such that the networks' processing is divided in two stages: the learning stage, where the network converges to a specific quantum…

Quantum mechanics is characterized by quantum coherence and entanglement. After having discovered how these fundamental concepts govern physical reality, scientists have been devoting intense efforts to harness them to shape future science…

This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…

A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in $2$D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant…

We introduce a notion of quantum function, and develop a compositional framework for finite quantum set theory based on a 2-category of quantum sets and quantum functions. We use this framework to formulate a 2-categorical theory of quantum…