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The system of two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem already addressed by many authors that we present here in some fresh points of view and carry on smoothly a whole…
We propose an adaptation of the notion of scaling symmetries for the case of Lie-Hamilton systems, allowing their subsequent reduction to contact Lie systems. As an illustration of the procedure, time-dependent frequency oscillators and…
Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time…
Synthetic dimensions based on particles' internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological…
We present a general strategy to simulate a D+1-dimensional quantum system using a D-dimensional one. We analyze in detail a feasible implementation of our scheme using optical lattice technology. The simplest non-trivial realization of a…
The adiabatic theorem is a fundamental result established in the early days of quantum mechanics, which states that a system can be kept arbitrarily close to the instantaneous ground state of its Hamiltonian if the latter varies in time…
Topological crystalline states are short-range entangled states jointly protected by onsite and crystalline symmetries. While the non-interacting limit of these states, e.g., the topological crystalline insulators, have been intensively…
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…
Contact geometry allows to describe some thermodynamic and dissipative systems. In this paper we introduce a new geometric structure in order to describe time-dependent contact systems: cocontact manifolds. Within this setting we develop…
We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…
We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose…
It is well known that typical Hamiltonian systems have divided phase space consisting of regions with regular dynamics on KAM tori and region(s) with chaotic dynamics called chaotic sea(s). This complex structure makes rigorous analysis of…
We discuss higher-dimensional gravitational instantons by studying appropriate self-duality equations for the spin connection. In seven and in eight dimensions, the corresponding spaces admit a covariantly constant spinor and have…
We report the observation of a symmetry-protected topological time crystal, which is implemented with an array of programmable superconducting qubits. Unlike the time crystals reported in previous experiments, where spontaneous breaking of…
Combining physical and synthetic dimensions allows a controllable realization and manipulation of high dimensional topological states. In our work, we introduce two quasiperiodically driven 1D systems which enable tunable topological energy…
A cascade of phase transitions from square to hexagonal lattice is studied in 2D system of particles interacting via core-softened potential. Due to the presence of two length-scales of repulsion, different local configurations with four,…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
We establish a link between metastability and a discrete time-crystalline phase in a periodically driven open quantum system. The mechanism we highlight requires neither the system to display any microscopic symmetry nor the presence of…
Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes like star formation and merging events. Recent studies show…
The circuit-to-Hamiltonian construction translates dynamics (a quantum circuit and its output) into statics (the groundstate of a circuit Hamiltonian) by explicitly defining a quantum register for a clock. The standard Feynman-Kitaev…