A. Rivero
The level splitting formula of an asymmetric double well potential is calculated taking into account the multi-instanton contributions (dilute gas approximation). Results can be related with known semiclassical ones obtained with a truncated hamiltonian, and the symmetric case is easily recovered.
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We present a new way to compute and interpret quantum tunneling in a 1-D double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of 1e-5. In contrast to the classical potential, the quantum potential has a triple-well if the classical wells are deep enough. Its minima are located at the position of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reprod…
We develop an instantonic calculus to derive an analytical expression for the thermally-assisted tunneling decay rate of a metastable state in a fully connected quantum spin model. The tunneling decay problem can be mapped onto the Kramers escape problem of a classical random dynamical field. This dynamical field is simulated efficiently by path integral Quantum Monte Carlo (QMC). We show analytically that the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the escape rate of the QMC process are identical. We relate this effect to the existence…
Quantum Simulation of Energy Bifurcation and Z_2-Symmetry Restoration in Macroscopic Quantum Tunneling
本文通过量子拉比模型模拟宏观量子隧穿中的瞬子效应，展示了能量分岔与自发对称性破缺，并揭示了瞬子贡献如何恢复对称性。
We use an instanton approximation to the continuous-time spin coherent-state path integral to obtain the tunnel splitting of classically degenerate ground states. We show that provided the fluctuation determinant is carefully evaluated, the path integral expression is accurate to order O(1/j). We apply the method to the LMG model and to the molecular magnet Fe_8 in a transverse field.
Ring-polymer instanton theory for tunneling between asymmetric wells
针对原始瞬子理论无法计算非对称双势阱隧穿裂分的问题，提出基于投影通量关联函数的新公式，经模型验证精度较高，成功应用于α-葑醇隧穿研究并厘清隧穿裂分与反应速率的关系。
A new method is used to investigate the tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. The nonlinear interaction between the atoms in each well contributes to a finite chemical potential, which, with consideration of periodic instantons, leads to a remarkably high tunneling frequency. This result can be used to interpret the newly found Macroscopic Quantum Self Trapping (MQST) effect. Also a new kind of first-order crossover between different regions is predicted.
From Quantum Tunneling to Classical Optimization through Instantons
本研究通过瞬子分析证明路径积分随机梯度下降（PISGD）可继承量子隧穿机制，其逃逸时间随反弹作用量而非势垒高度指数增长，数值实验验证了该缩放，但不排除量子算法存在潜在优势。
We consider tunneling processes in QFT induced by collisions of elementary particles. We propose a semiclassical method for estimating the probability of these processes in the limit of very high collision energy. As an illustration, we evaluate the maximum probability of induced tunneling between different vacua in a (1+1)-dimensional scalar model with boundary interaction.
Perturbatively corrected ring-polymer instanton rate theory rigorously captures anharmonicity and deep tunneling
本研究推导环聚合物框架下的微扰校正瞬子速率理论RPI+PC，通过势能高阶导数校正垂直隧穿路径的非谐性，无需全局势能面，经理论推导与模型反应验证，系统性提升了瞬子理论的速率计算精度。
An instanton method is proposed to investigate the quantum tunneling between two weakly-linked Bose-Einstein condensates confined in double-well potential traps. We point out some intrinsic pathologies in the earlier treatments of other authors and make an effort to go beyond these very simple zero order models. The tunneling amplitude may be calculated in the Thomas-Fermi approximation and beyond it; we find it depends on the number of the trapped atoms, through the chemical potential. Some suggestions are given for the observation of the Josephson oscillation and the MQST.
We study the quantum-mechanical tunneling phenomenon in models which include the existence of non-equivalent vacua. For such a purpose we evaluate the euclidean propagator between two minima of the potential at issue in terms of the quadratic fluctuations over the corresponding instantons. The effect of the multi-instanton configurations are included by means of the alternate dilute-gas approximation.
Instantons meet resonances: Unifying two seemingly distinct approaches to quantum tunneling
本文通过展示共振态方法与瞬子方法的等价性，统一了两种看似不同的量子隧穿理论框架。
Coupled Instantons In A Four-Well Potential With Application To The Tunneling Of A Composite Particle
本文研究了四井势中耦合瞬子的特性，并应用于一维复合粒子的隧穿问题。
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.
Quantum tunneling of vortices has been found to be an important novel phenomena for description of low temperature creep in high temperature superconductors (HTSCs). We speculate that quantum tunneling may be also exhibited in mesoscopic superconductors due to vortices trapped by the Bean-Livingston barrier. The London approximation and method of images is used to estimate the shape of the potential well in superconducting HTSC quantum dot. To calculate the escape rate we use the instanton technique. We model the vortex by a quantum particle tunneling from a two-dimensional ground state under …
The tunneling decay event of a metastable state in a fully connected quantum spin model can be simulated efficiently by path integral quantum Monte Carlo (QMC) [Isakov $et~al.$, Phys. Rev. Lett. ${\bf 117}$, 180402 (2016).]. This is because the exponential scaling with the number of spins of the thermally-assisted quantum tunneling rate and the Kramers escape rate of QMC are identical [Jiang $et~al.$, Phys. Rev. A ${\bf 95}$, 012322 (2017).], a result of a dominant instantonic tunneling path. In Ref. [1], it was also conjectured that the escape rate in open-boundary QMC is quadratically larger…
False vacuum decay of excited states in finite-time instanton calculus
本研究针对泛函方法无法测定激发态衰变宽度的问题，提出基于有界时间区间的复合路径积分方法，结合激发态波函数近似计算衰变宽度及其主导量子修正，验证了与WKB结果的一致性，修正了既往研究的缺陷。
Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis
本文用保持时间实数、向 Hamiltonian 加入无穷小复正则项的实时间路径积分方法，从双势阱模型恢复激发态隧穿的类瞬子图像。
Gaussian fluctuations in the tunneling probability of a closed universe
本文基于欧几里得路径积分法，推导了闭合宇宙量子创生的隧道概率表达式，考虑了高斯涨落对隧道概率的修正，提供了更精确的 semiclassical 估计。
By using a usual instanton method we obtain the energy splitting due to quantum tunneling through the triple well barrier. It is shown that the term related to the midpoint of the energy splitting in propagator is quite different from that of double well case, in that it is proportional to the algebraic average of the frequencies of the left and central wells.
Real-Time Instantons in Complex-Driven Qubits
本文研究复耦合周期驱动的量子拉比模型，发现非幺正相干驱动产生单向瞬子解，实现快速确定性隧穿至基态，提供无需耗散浴的PT对称高保真量子比特重置方法，并可将吸引子置于布洛赫球任意点。
We consider induced topological transitions in a wire made from cylindrical superconducting film. During a transition, a pulse of electric current causes transport of a virtual vortex-antivortex pair around the cylinder. We consider both the instanton approach, in which the transition is viewed as motion of vortices in the Euclidean time, and the real-time dual formulation, in which vortices are described by a fundamental quantum field. The instanton approach is convenient to discuss effects of the environment, while in the dual formulation we show that there exists a potentially useful adiaba…
In this work, we study the $ U(1)/Z_2 $ Dicke model at a finite $ N $ by using the $ 1/J $ expansion and exact diagonization. This model includes the four standard quantum optics model as its various special limits. The $ 1/J $ expansions is complementary to the strong coupling expansion used by the authors in arXiv:1512.08581 to study the same model in its dual $ Z_2/U(1) $ representation. We identify 3 regimes of the system's energy levels: the normal, $ U(1) $ and quantum tunneling (QT) regime. The system's energy levels are grouped into doublets which consist of scattering states and Schro…
Photon-instanton scattering in a superconducting circuit: Beyond the very high impedance regime
针对超导电路中瞬子散射理论仅适用于极高阻抗区域的局限，本文引入数值方法消除近似，在无拟合参数下提高了与实验测量的一致性，拓展了其适用范围。
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