Quantum Tunneling Probability Research Articles

Anti-[formula omitted] transformations and complex non-Hermitian [formula omitted]-symmetric superpartners

We propose a new algebraic formalism for constructing complex non-Hermitian PT-symmetric superpartners by extending a conventional shape-invariant superpotential into the complex domain. The resulting potential is an unbroken super- and parity-time (PT)-symmetric shape-invariant potential with real energy eigenvalues, maintaining this property for all parameter values. In order to restore the probabilistic interpretation within a true quantum theory, a new inner product called the CPT-inner product is defined in PT-symmetric quantum mechanics, replacing the Dirac Hermitian inner product. In this work, we propose a new version of the inner product called the anti-PT (APT)-inner product, 〈A|B〉≡|A〉APT.|B〉, which replaces the previous versions without any additional considerations. This PT-supersymmetric quantum mechanics framework also allows for the unification of various areas of physics, including classical optics and quantum mechanics. To validate the theory, we present exact solutions for optical waveguides and the quantum tunneling probability, demonstrating excellent agreement with experimental data for the probability of crossing the potential barrier in the 3H(d,n)4He reaction.

Microscopic Quantum Transport Processes of Out‐of‐Plane Charge Flow in 2D Semiconductors Analyzed by a Fowler–Nordheim Tunneling Probe

AbstractWeak interlayer couplings at 2D van der Waals (vdW) interfaces fundamentally distinguish out‐of‐plane charge flow, the information carrier in vdW‐assembled vertical electronic and optical devices, from the in‐plane band transport processes. Here, the out‐of‐plane charge transport behavior in 2D vdW semiconducting transition metal dichalcogenides (SCTMD) is reported. The measurements demonstrate that, in the high electric field regime, especially at low temperatures, either electron or hole carrier Fowler–Nordheim (FN) tunneling becomes the dominant quantum transport process in ultrathin SCTMDs, down to monolayers. For few‐layer SCTMDs, sequential layer‐by‐layer FN tunneling is observed to dominate the charge flow, thus serving as a material characterization probe for addressing the Fermi level positions and the layer numbers of the SCTMD films. Furthermore, it is shown that the physical confinement of the electron or hole carrier wave packets inside the sub‐nm thick semiconducting layers reduces the vertical quantum tunneling probability, leading to an enhanced effective mass of tunneling carriers.

Enhanced quantum tunneling in quantum Zeno dynamics freezing the momentum direction

Quantum tunneling is a fundamental quantum mechanical effect involved in plenty of physical phenomena. Its control would impact these phenomena and the technologies based on them. We show that the quantum tunneling probability through a potential barrier can be increased to approach unity in a quantum Zeno dynamics undergone by the tunneling particle in which the direction of the momentum is frequently monitored. We first model the measurements of the momentum direction as selective von Neumann projections, and then as nonselective, direction-sensitive interactions of the particle with probe particles. Nonselective measurements are more efficient than selective measurements in enhancing the quantum tunneling probability.

GABA Receptors Can Depolarize the Neuronal Membrane Potential via Quantum Tunneling of Chloride Ions: A Quantum Mathematical Study.

GABA (gamma-aminobutyric acid) receptors represent the major inhibitory receptors in the nervous system and their inhibitory effects are mediated by the influx of chloride ions that tends to hyperpolarize the resting membrane potential. However, GABA receptors can depolarize the resting membrane potential and thus can also show excitatory effects in neurons. The major mechanism behind this depolarization is mainly attributed to the accumulation of chloride ions in the intracellular compartment. This accumulation leads to increase in the intracellular chloride concentration and depolarize the Nernst potential of chloride ions. When the membrane potential is relatively hyperpolarized, this will result in a chloride efflux instead of influx trying to reach their depolarized equilibrium potential. Here, we propose different mechanism based on a major consequence of quantum mechanics, which is quantum tunneling. The quantum tunneling model of ions is applied on GABA receptors and their corresponding chloride ions to show how chloride ions can depolarize the resting membrane potential. The quantum model states that intracellular chloride ions have higher quantum tunneling probability than extracellular chloride ions. This is attributed to the discrepancy in the kinetic energy between them. At physiological parameters, the quantum tunneling is negligible to the degree that chloride ions cannot depolarize the membrane potential. Under certain conditions such as early neuronal development, gain-of-function mutations, stroke and trauma that can lower the energy barrier of the closed gate of GABA receptors, the quantum tunneling is enhanced so that the chloride ions can depolarize the resting membrane potential. The major unique feature of the quantum tunneling mechanism is that the net efflux of chloride ions is attained without the need for intracellular accumulation of chloride ions as long as the energy barrier of the gate is reduced but still higher than the kinetic energy of the chloride ion as a condition for quantum tunneling to take place.

Polariton condensate and Landau-Zener-Stückelberg interferometry transition in multilayer transition metal dichalcogenides

This paper gives a detailed description of a high-performance polariton condensate for a quantum mechanical two-level system (TLS). We propose a transition metal dichalcogenides (TMDs) setup and theoretically carry out the spectroscopy of these polariton condensates. Through theoretical and numerical analysis, we obtain many features in two dimensional (2D) multilayer TMDs. We compute the energy of the system and the Landau-Zener-Stückelberg (LZS) quantum tunneling probability under the effect of a sequence of laser light. At certain critical 2D TMDs parameters, the system exhibits a multi-crossing scenario in a privileged position of 2D multilayer TMDs. We predict the consecutive modulations and highlight the conservation of the LZS interference patterns mapped from the 2D TMDs system. At weak coupling regime, a successful conversion of interferometry signals is identified for some values of laser frequency. We explain such a result as a valley sensitive cavity rate model due to coherent exchange and incoherent scattering, meaning that polariton condensate is formed in the valley around the Brillouin zone. The latter is used quantitatively and qualitatively to achieve high-precision measurements beyond that of its elementary constituents. The obtained results confirm that has the highest sensitivity to radiation field as compared to other 2D multilayer TMDs materials. Therefore, stands as an appropriate candidate among other 2D TMDs to form polariton condensates.

Recombination of Polaronic Electron-Hole Pairs in Hematite Determined by Nuclear Quantum Tunneling.

Here, we investigate the intrinsic nonradiative recombination mechanism in hematite single crystals that decides the photocarrier lifetime under solar illumination. On the basis of the small polaron theory, we propose that the photogenerated electron-hole pair along with its induced lattice deformation in hematite could be treated as a pseudocoordination-complex (PCC) dispersed in a solid medium. We demonstrate that the nonradiative recombination rate at different temperatures determined from the transient absorption spectroscopy can be excellently described by the nonradiative transition theory developed previously for parallels of the PCC model. Our finding suggests that at room temperature the nonradiative recombination in hematite substantially depends on the probability of quantum tunneling of the nuclear configuration.

Dynamics of the isotope exchange reaction of D with H3 +, H2D+, and D2H.

We have measured the merged-beams rate coefficient for the titular isotope exchange reactions as a function of the relative collision energy in the range of ∼3 meV-10 eV. The results appear to scale with the number of available sites for deuteration. We have performed extensive theoretical calculations to characterize the zero-point energy corrected reaction path. Vibrationally adiabatic minimum energy paths were obtained using a combination of unrestricted quadratic configuration interaction of single and double excitations and internally contracted multireference configuration interaction calculations. The resulting barrier height, ranging from 68 meV to 89 meV, together with the various asymptotes that may be reached in the collision, was used in a classical over-the-barrier model. All competing endoergic reaction channels were taken into account using a flux reduction factor. This model reproduces all three experimental sets quite satisfactorily. In order to generate thermal rate coefficients down to 10 K, the internal excitation energy distribution of each H3 + isotopologue is evaluated level by level using available line lists and accurate spectroscopic parameters. Tunneling is accounted for by a direct inclusion of the exact quantum tunneling probability in the evaluation of the cross section. We derive a thermal rate coefficient of <1×10-12 cm3 s-1 for temperatures below 44 K, 86 K, and 139 K for the reaction of D with H3 +, H2D+, and D2H+, respectively, with tunneling effects included. The derived thermal rate coefficients exceed the ring polymer molecular dynamics prediction of Bulut et al. [J. Phys. Chem. A 123, 8766 (2019)] at all temperatures.

Role of Potassium Ions Quantum Tunneling in the Pathophysiology of Phantom Limb Pain.

(1) Background: multiple theories were proposed to explain the phenomenon of phantom limb pain (PLP). Nevertheless, the phenomenon is still shrouded in mystery. The aim of this study is to explore the phenomenon from a new perspective, where quantum tunneling of ions, a promising field in medical practice, might play a major role. (2) Methods: investigators designed a quantum mathematical model based on the Schrödinger equation to examine the probability of potassium ions quantum tunneling through closed membrane potassium channels to the inside of phantom axons, leading to the generation of action potential. (3) Results: the model suggests that the probability of action potential induction at a certain region of the membrane of phantom neurons, when a neuron of the stump area is stimulated over 1 mm2 surface area of the membrane available for tunneling is 1.04 × 10−2. Furthermore, upon considering two probabilities of potassium channelopathies, one that decreased the energy of the barrier by 25% and another one by 50%, the tunneling probability became 1.22 × 10−8 and 3.86 × 10−4, respectively. (4) Conclusion: quantum models of potassium ions can provide a reliable theoretical hypothesis to unveil part of the ambiguity behind PLP.

The Effect of Basis Set on Quantum Tunneling Probability with the Case of trans-HCOH Isomerization

We investigate the effects of basis set in quantum tunneling probability in the case of trans-HCOH isomerization to H2CO. Based on Density Functional Theory (DFT) calculation with B3LYP as functional exchange-correlation and 6-31G(d, p) as basis set, Rizka et al. found that trans-HCOH molecule has half life for 2.5 hours. The result has 0.7 hour longer than experimental result done by Schreiner et al. In this study, we used five variations of basis set which are: STO-3G, 6-31G, 6-31G(d, p), 6-31+G(d, p), and LANL2DZ. We started to investigate the effects of basis set on the electronic structure and vibrational frequency of the molecules. Then, we investigated the effects of basis set on quantum tunneling probability in molecule. Based on quantum tunneling probabilities, we could calculate half-life of trans-HCOH isomerization to H2CO. We compare our results to the experimental result done by Schreiner et al. The results show that basis set increases the quantum tunneling probability of the isomerization.

Approximation Rectangular Function as Potential Barrier

Quantum tunneling occurs in the isomerization of hydroxymethylene into formaldehyde. Experiments and theory have proven the occurrence of it but both of them have a different result of the half-life of 0.7 hours. The differences the result is the motivation in this study. In theoretical, the probability of quantum tunneling calculates by Wentzel, Kreamer, Berlioun (WKB) approximation. This study calculates probability quantum tunneling use WKB and rectangular function approximation. The calculation of quantum tunneling probability with rectangular function approximation started at 1, 3, 5, 7 until 59 rectangular functions potential barrier use transfer matrix method to simplify the calculation. We use Gaussian function as the potential barrier that the height and width of the potential barrier satisfy the character of the potential barrier in isomerization hydroxymethylene barrier to formaldehyde. And the result, we get the minimum number of rectangular potential barrier to obtain a stable quantum tunneling probability value of 35 potential.

Influence of magnetic dilution on relaxation processes in a solid solution comprising tetrahedral Co/ZnII complexes.

Single ion magnets have long been considered good prospective candidates to record a bit of information. One of the smallest known single ion magnets is CoBr2(pyridine)2. This molecular compound exhibits slow relaxation of magnetization mainly due to the thermally activated Orbach process, [A. M. Majcher et al., Chem. Sci., 2018, 9, 7277-7286]. However, the total relaxation time is dramatically shortened at low temperatures due to the direct, Raman, and quantum tunneling of magnetization processes. At low temperatures, the distribution of the probability of the possible relaxation pathways in this case favours QTM and the direct process over the Orbach process. To prolong the relaxation time, the compound was diluted with diamagnetic ZnII, producing 5 analogues of the general formula: CoxZn1-xBr2(pyridine)2 (x = 0.91, 0.67, 0.43, 0.24, and 0.06), confirmed to be a solid solution by independent experimental techniques (powder X-ray diffraction, infrared spectroscopy). The presence of diamagnetic ZnII ions changes the distribution of the dipolar interactions between the CoII centres in the material, which results in a monotonous change in the relaxation times, which in turn become longer with increasing dilutions, which is explained by the diminishing QTM contribution. The appearance of multiple relaxation processes is also observed for higher x, which is explained as the creation of multiple, separate frequency domains, as a result of the competition between QTM and the direct process contributions. We present a thorough, systematic study of magnetic dilution, which will hopefully be useful to estimate optimal dilutions in similar solid solutions.

Higgs vacuum stability with vectorlike fermions

We present the effects of vector-like fermions (VLF) on the stability of the Higgs electroweak vacuum, using the renormalization group improved Higgs effective potential. We review the calculation of the one-loop beta-functions of the standard model couplings, paying particular attention to the fermion contributions. From this, we derive the VLF contributions to the beta-functions. We also include the significant two-loop contributions to the beta-functions. Using these beta-functions we determine the scale at which the effective Higgs quartic-coupling becomes zero and goes negative, signaling vacuum instability. We find that for certain VLF masses and Yukawa couplings, the Higgs quartic stays positive for field values all the way up to the Planck scale, implying that the meta-stable vacuum of the standard model can be rendered absolutely stable if VLFs are present with certain parameters. For other values of VLF parameters, the Higgs vacuum is metastable as in the standard model. For cases where the vacuum is metastable, we compute the probability of quantum tunneling from the false electroweak vacuum into a deeper true vacuum in our Hubble volume by numerically solving for the bounce configuration in Euclidean space-time and computing the bounce action for it. We compare our numerical solution with the analytical approximation for the bounce action commonly used in the literature and comment on when the latter may be used.

Landau-Zener tunneling of qubit states and Aharonov-Bohm interferometry in double quantum wires

This paper gives a detailed description of a high-performance tunneling wire “flying qubit” for a quantum mechanical two-level system. We propose a simple double-wire interferometer setup and theoretically carry out the spectroscopy of these flying qubits. As such, we present a tight binding theoretical model which effectively mimicks the experimental setup and then compute the energy diagram and the Landau-Zener quantum tunneling probability under the effect of a sequence of magnetic pulses and gate voltages. At certain critical electrostatic gate voltages, the system exhibits a step rise in the Landau-Zener tunneling transition by playing a multi-crossing scenario in a privileged position of two geometric wires. We predict the consecutive modulations and precise the conservation of the Landau-Zener-Stückelberg-Majorana interference patterns mapped from the two-terminal of the double-wire system. A successful conversion of interferometry signals is identified within the two-path interferometer with higher intrinsic quantum correction errors. The latter is used quantitatively and qualitatively to achieve high-precision measurements beyond the standard Landau-Zener limit. The obtained results confirm the possibility of the construction of Aharonov-Bohm interferometers following the proposed model.

Quantum tunneling dynamics in symmetrical driven double well system based on Husimi representation

In present study, the quantum tunneling process in symmetrical driven double-well system is studied by using the entangled trajectory molecular dynamics method based on the Husimi representation. Quantum tunneling dynamics show three different physical mechanisms vary with the amplitude and frequency of driven force: reposeful tunneling, chaos-assisted tunneling, oscillatory tunneling. Different form other methods, quantum underline dynamics process are explored by showing entangled trajectory in the phase space. We show chaotic behavior of entangled trajectories in the phase space, and the quantum tunneling process is vividly shown by comparing entangled trajectory with the classical trajectory with the same initial state. Furthermore, we discuss the effect of symmetry breaking on the potential to the quantum dynamical process, quantum tunneling probability will be remarkably reduced by breaking potential’s symmetry. Finally, the suppression of quantum wave packet tunneling under strong force is presented.

Comparison of the Magnetic Anisotropy and Spin Relaxation Phenomenon of Dinuclear Terbium(III) Phthalocyaninato Single-Molecule Magnets Using the Geometric Spin Arrangement.

Herein we report the synthesis and characterization of a dinuclear TbIII single-molecule magnet (SMM) with two [TbPc2]0 units connected via a fused-phthalocyaninato ligand. The stable and robust complex [(obPc)Tb(Fused-Pc)Tb(obPc)] (1) was characterized by using synchrotron radiation measurements and other spectroscopic techniques (ESI-MS, FT-IR, UV). The magnetic couplings between the TbIII ions and the two π radicals present in 1 were explored by means of density functional theory (DFT). Direct and alternating current magnetic susceptibility measurements were conducted on magnetically diluted and nondiluted samples of 1, indicating this compound to be an SMM with improved properties compared to those of the well-known [TbPc2]-/0/+ and the axially symmetric dinuclear TbIII phthalocyaninato triple-decker complex (Tb2(obPc)3). Assuming that the probability of quantum tunneling of the magnetization (QTM) occurring in one TbPc2 unit is PQTM, the probability of QTM simultaneously occurring in 1 is PQTM2, meaning that QTM is effectively suppressed. Furthermore, nondiluted samples of 1 underwent slow magnetic relaxation times (τ ≈ 1000 s at 0.1 K), and the blocking temperature (TB) was determined to be ca. 16 K with an energy barrier for spin reversal (Ueff) of 588 cm-1 (847 K) due to D4d geometry and weak inter- and intramolecular magnetic interactions as an exchange bias (Hbias), reducing QTM. Four hyperfine steps were observed by micro-SQUID measurement. Furthermore, solution NMR measurements (one-dimensional, two-dimensional, and dynamic) were done on 1, which led to the determination of the high rotation barrier (83 ± 10 kJ/mol) of the obPc ligand. A comparison with previously reported TbIII triple-decker compounds shows that ambient temperature NMR measurements can indicate improvements in the design of coordination environments for SMMs. A large Ueff causes strong uniaxial magnetic anisotropy in 1, leading to a χax value (1.39 × 10-30 m3) that is larger than that for Tb2(obPc)3 (0.86 × 10-30 m3). Controlling the coordination environment and spin arrangement is an effective technique for suppressing QTM in TbPc2-based SMMs.

A Theoretical Study of the Rearranging Trans-HCOH to H2CO via Quantum Tunneling with DFT and WKB Approximation

We attempt to study the stability of trans-HCOH molecule using density functional theory (DFT). Experimentally, trans-HCOH rearranges to H2CO with half life two hours in temperature at 11K whereby quantum tunneling makes the rearrangement possible. We begin from determination of reaction path from trans-HCOH to H2CO followed by its corresponding energy barrier using DFT. Then, we use Wentzel-Kramers-Brillouin (WKB)approximation to get probability of quantum tunneling hence we are able to calculate the rearrangement rate and the half life. To prove the rearrangement is not triggered by internal thermal energy, we calculate rearrangement rate based on the Arrhenius equation. Our calculations predict the halflife of trans-HCOH is 151 minutes (2.5 hours) via quantum tunneling and infinity via internal thermal energy which agrees with the experiment.

A Theoretical Study of Monodeuteriation Effect on the Rearrangement of Trans-HCOH to H2CO via Quantum Tunneling with DFT and WKB Approximation

We study the effect of replacing hydrogen atom with deuterium (monodeuteriation) on the stability of trans-HCOH using density functional theory. The study begins by verifying that the monodeuteriation does not affect the electronic structure, but it does the vibrational frequency of the molecule. The potential barrier function is predicted using intrinsic reaction coordinate calculation and we use the predicted potential function to calculate the quantum tunneling probability using Wentzel-Kramers-Brillouin(WKB)approximation. We demonstrate the monodeuteration decreases the molecule's vibrational frequency as well as the quantum tunneling probability. The half-life calculation after monodeuteration is 2.97 × 1016 hours, which is extremely longer than before monodeuteration that is only 2.5 hours using the same calculation methods.

The Hawking temperature of a dynamical black hole in de Sitter spacetime

The Hawking radiation near the horizon of a black hole is derived by the surface gravity in both dynamical and stationary cases. Also, the quantum tunneling probability through the potential near the horizon gives the Hawking temperature, when we use the Hamilton-Jacobi equation or the Hamilton equations. In the case of a dynamical black hole in de Sitter spacetime, which is similar to a Schwarzschild-de Sitter black hole, the spacetime has two horizons, the black-hole and cosmological ones. We consider the Hawking temperature of the spacetime with two horizons by using two different methods. The temperature for the equilibrium state in this spacetime is calculated by using the tunneling method.

Nonlocal and quantum-tunneling contributions to harmonic generation in nanostructures: Electron-cloud-screening effects

Our theoretical examination of second and third harmonic generation from metal-based nanostructures predicts that nonlocal and quantum tunneling phenomena can significantly exceed expectations based solely on local, classical electromagnetism. Mindful that the diameter of typical transition metal atoms is approximately 3{\AA}, we adopt a theoretical model that treats nanometer-size features and/or sub-nanometer size gaps or spacers by taking into account: (i) the limits imposed by atomic size to fulfill the requirements of continuum electrodynamics; (ii) spillage of the nearly-free electron cloud into the surrounding vacuum; and (iii) the increased probability of quantum tunneling as objects are placed in close proximity. Our approach also includes the treatment of bound charges, which add crucial, dynamical components to the dielectric constant that are neglected in the conventional hydrodynamic model, especially in the visible and UV ranges, where interband transitions are important. The model attempts to inject into the classical electrodynamic picture a simple, perhaps more realistic description of the metal surface by incorporating a thin patina of free-electrons that screens an internal, polarizable medium.

Improved Multidimensional Semiclassical Tunneling Theory

We show that the analytic multidimensional semiclassical tunneling formula of Miller et al. [Miller, W. H.; Hernandez, R.; Handy, N. C.; Jayatilaka, D.; Willets, A. Chem. Phys. Lett. 1990, 172, 62] is qualitatively incorrect for deep tunneling at energies well below the top of the barrier. The origin of this deficiency is that the formula uses an effective barrier weakly related to the true energetics but correctly adjusted to reproduce the harmonic description and anharmonic corrections of the reaction path at the saddle point as determined by second order vibrational perturbation theory. We present an analytic improved semiclassical formula that correctly includes energetic information and allows a qualitatively correct representation of deep tunneling. This is done by constructing a three segment composite Eckart potential that is continuous everywhere in both value and derivative. This composite potential has an analytic barrier penetration integral from which the semiclassical action can be derived and then used to define the semiclassical tunneling probability. The middle segment of the composite potential by itself is superior to the original formula of Miller et al. because it incorporates the asymmetry of the reaction barrier produced by the known reaction exoergicity. Comparison of the semiclassical and exact quantum tunneling probability for the pure Eckart potential suggests a simple threshold multiplicative factor to the improved formula to account for quantum effects very near threshold not represented by semiclassical theory. The deep tunneling limitations of the original formula are echoed in semiclassical high-energy descriptions of bound vibrational states perpendicular to the reaction path at the saddle point. However, typically ab initio energetic information is not available to correct it. The Supporting Information contains a Fortran code, test input, and test output that implements the improved semiclassical tunneling formula.