Abrupt termination of a quantum channel and exactly solvable position-dependent mass models in three dimensions

A solvable model of quantum random optimization problems

We study the quantum version of a simplified model of optimization problems, where quantum fluctuations are introduced by a transverse field acting on the qubits. We find a complex low-energy spectrum of the quantum Hamiltonian, characterized by an abrupt condensation transition and a continuum of level crossings as a function of the transverse field. We expect this complex structure to have deep consequences on the behavior of quantum algorithms attempting to find solutions to these problems.

The Lambert-W step-potential - an exactly solvable confluent hypergeometric potential

We present an asymmetric step-barrier potential for which the one-dimensional stationary Schrödinger equation is exactly solved in terms of the confluent hypergeometric functions. The potential is given in terms of the Lambert -function, which is an implicitly elementary function also known as the product logarithm. We present the general solution of the problem and consider the quantum reflection at transmission of a particle above this potential barrier. Compared with the abrupt-step and hyperbolic tangent potentials, which are reproduced by the Lambert potential in certain parameter and/or …

Exactly solvable pairing models in two dimensions

The BCS theory models electron correlations with pure zero-momentum pairs. Here we consider a family of pairing Hamiltonians, where the electron correlations are modelled with pure arbitrary-momentum pairs. We find all models in the family are exactly solvable, and present these solutions. It is interesting to note that the $η$ pair or the $d$ -wave pair condensate in $T_{c}$ superconductivity can be the ground state of a Hamiltonian in the family. These models are two-dimensional because only the z-component of the total electron spin $S_z$ is conserved. Significantly, for the $η$ pair or $d$…

Transient noise spectra in resonant tunneling setups: Exactly solvable models

We investigate the transient evolution of finite-frequency current noise after abrupt switching on of the tunneling coupling in two paradigmatic, exactly solvable models of mesoscopic physics: the resonant level model and the Majorana resonant level model, which emerges as an effective model for a Kondo quantum dot at the Toulouse point. We find a parameter window in which the transient noise can become negative, a property it shares with the transient current. However, in contrast to the transient current, which approaches the steady state exponentially fast, we observe an algebraic decay in …

量子达尔文主义–编码转变的一个可解模型

A Solvable Model of Quantum Darwinism-Encoding Transitions

本文构建扩张树上随机 Clifford 电路的可解模型，刻画量子达尔文主义相与编码相之间由混合相和两个连续转变分隔的结构，并用双副本及环境窃听模型联系 MIPT。

An Exactly Solvable Model for a $4+1D$ Beyond-Cohomology Symmetry Protected Topological Phase

We construct an exactly solvable commuting projector model for a $4+1$ dimensional ${\mathbb Z}_2$ symmetry-protected topological phase (SPT) which is outside the cohomology classification of SPTs. The model is described by a decorated domain wall construction, with "three-fermion" Walker-Wang phases on the domain walls. We describe the anomalous nature of the phase in several ways. One interesting feature is that, in contrast to in-cohomology phases, the effective ${\mathbb Z}_2$ symmetry on a $3+1$ dimensional boundary cannot be described by a quantum circuit and instead is a nontrivial quan…