Related papers: Quantum mechanical bootstrap without inequalities:…
Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries. In the non-Abelian case, the broken higher-form symmetries are notably non-invertible. In this work, we extend this framework to mixed states,…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
We analyze thermal correlators in the Sachdev-Ye-Kitaev model away from the maximally chaotic limit. Despite the absence of a weakly curved black hole dual, the two point function decomposes into a sum over a discrete set of quasinormal…
Quantum mechanics implies that not all physical properties can be simultaneously well defined, such as the momentum and position due to Heisenberg uncertainty principle. Some alternative theories have been explored, notably the…
Recently, an interesting form of non-classical effect which can be considered as a form of contextuality within quantum mechanics, has been demonstrated for a four-level system by discriminating the different routes that are taken for…
A nonpertubative approach to quantum gravity using precanonical field quantization originating from the covariant De Donder-Weyl Hamiltonian formulation which treats space and time variables on equal footing is presented. A generally…
This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a…
Sachdev-Ye-Kitaev (SYK) model has emerged as a new paradigm of the non-Fermi-liquid behavior. Here we investigate a possibility of having a superconducting off-diagonal long-range order (ODLRO) and a pseudogap phase within the SYK…
A bootstrap program is presented for algebraically solving the $R$-matrix of a generic integrable quantum spin chain from its Hamiltonian. The Yang-Baxter equation contains an infinite number of seemingly independent constraints on the…
The concept of supersymmetry in a quantum mechanical system is extended, permitting the recognition of many more supersymmetric systems, including very familiar ones such as the free particle. Its spectrum is shown to be supersymmetric,…
Within the quantum field-theoretical approach describing the evolution of a quadratic Liouvillian in the basis of Keldysh contour coherent states, we investigate the spectral and transport properties of a dissipative superconducting system…
The Sachdev-Ye-Kitaev (SYK) model provides an analytically tractable framework for exotic strongly correlated phases where conventional paradigms like Landau's Fermi liquid theory collapse. This review offers a pedagogical introduction to…
We compute the phase diagram of a $\text{U}(N)^{2}\times\text{O}(D)$ invariant fermionic planar matrix quantum mechanics [equivalently tensor or complex Sachdev-Ye-Kitaev (SYK) models] in the new large $D$ limit, dominated by melonic…
We point out that the bootstrap program in quantum mechanics proposed by Han et al reduces to a bootstrap study of a microcanonical ensemble of the same Hamiltonian in the $\hbar \to 0$ limit. In the limit, the quantum mechanical…
Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties.…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
We investigate the spontaneous parity-time (PT )-symmetry breaking and spectral properties of a PT symmetric quantum kicked rotor under resonance conditions. At resonance, the QKR reduces to a finite-dimensional system. In the localized…
We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…
Spontaneous symmetry breaking (SSB) is mathematically tied to some limit, but must physically occur, approximately, before the limit. Approximate SSB has been independently understood for Schroedinger operators with double well potential in…
Spontaneous symmetry breaking (SSB) is crucial to the occurrence of phase transitions. Once a phase transition occurs, a quantum system presents degenerate eigenstates that lack the symmetry of the Hamiltonian. After crossing the critical…