Cited by 4,572Atomic and Molecular PhysicsAdvanced Physical and Chemical Molecular InteractionsAdvanced Chemical Physics Studies

The DOI matches its Crossref record.

Non-adiabatic crossing of energy levels

Open access

Zener, Clarence·1932·Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character

DOI 10.1098/rspa.1932.0165

Open this paper in CoChat — free account

Abstract

Abstract The crossing of energy levels has been a matter of considerable discussion. The essential features may be illustrated in the crossing of a polar and homopolar state of a molecule. Let ψ1 (x/R), ψ2 (x/R) be two electronic eigenfunctions of a molecule with stationary nuclei. Let these eigenfunctions have the property that for R≫R0, ψ1 has polar characteristics, ψ2 homopolar; while at R≪R0, ψ2 has polar characteristics, ψ1 homopolar. In the region R=R0 these two eigenfunctions may be said to exchange their characteristics.

Integrity signals

Registry

Crossref · 10.1098/rspa.1932.0165

Cites

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Sorted by citations

Items 201–300 of 1,003

Quantum Control over Single Spins in Diamond
Dobrovitski, V. V., Fuchs, G. D., Falk, A. L., Santori, C., & Awschalom, D. D. (2013) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-030212-184238 · Cited by 180
Manipulating Quantum Structures Using Laser Pulses
Shore, B. W. (2011) · Cambridge University Press eBooks · doi:10.1017/cbo9780511675713 · Cited by 181
Non-Born–Oppenheimer trajectories with self-consistent decay of mixing
Zhu, C., Jasper, A. W., & Truhlar, D. G. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1648306 · Cited by 177
Quenching Processes in Hydrogen-Bonded Pairs: Interactions of Excited Fluorenone with Alcohols and Phenols
Biczók, L., Bérces, T., & Linschitz, H. (1997) · Journal of the American Chemical Society · doi:10.1021/ja972071c · Cited by 177
Correlation Function Approach to Radiationless Transitions
Fischer, S. F. (1970) · The Journal of Chemical Physics · doi:10.1063/1.1674470 · Cited by 178
Resonant Energy Transfer between Localized Electronic States in a Crystal
Soules, T. F., & Duke, C. B. (1971) · Physical review. B, Solid state · doi:10.1103/physrevb.3.262 · Cited by 176
Breakdown of a Mott Insulator: A Nonadiabatic Tunneling Mechanism
Oka, T., Arita, R., & Aoki, H. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.066406 · Cited by 176
Radio Signals from Axion Dark Matter Conversion in Neutron Star Magnetospheres
Hook, A., Kahn, Y. F., Safdi, B. R., et al. (2018) · Physical Review Letters · doi:10.1103/physrevlett.121.241102 · Cited by 176
Tunable Landau-Zener transitions in a spin-orbit-coupled Bose-Einstein condensate
Olson, A. J., Wang, S.-J., Niffenegger, R., Li, C.-H., Greene, C. H., & Chen, Y. P. (2014) · Physical Review A · doi:10.1103/physreva.90.013616 · Cited by 176
Multiscale Molecular Dynamics Simulations of Polaritonic Chemistry
Luk, H. L., Feist, J., Toppari, J. J., & Groenhof, G. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00388 · Cited by 177
Nonadiabatic processes involving quantum-like and classical-like coordinates with applications to nonadiabatic electron transfers
Marcus, R. A. (1984) · The Journal of Chemical Physics · doi:10.1063/1.447418 · Cited by 172
Asymmetric Landau-Zener Tunneling in a Periodic Potential
Jona-Lasinio, M., Morsch, O., Cristiani, M., et al. (2003) · Physical Review Letters · doi:10.1103/physrevlett.91.230406 · Cited by 173
State selective photodissociation dynamics of A state ammonia. II
Biesner, J., Schnieder, L., Ahlers, G., Xie, X., Welge, K. H., Ashfold, M. N. R., & Dixon, R. N. (1989) · The Journal of Chemical Physics · doi:10.1063/1.457644 · Cited by 174
Nonequilibrium Thermodynamics
Scherer, P. O. J., & Fischer, S. F. (2010) · Biological and medical physics series · doi:10.1007/978-3-540-85610-8_10 · Cited by 173
Role of phase coherence in the transition dynamics of a periodically driven two-level system
Kayanuma, Y. (1994) · Physical Review A · doi:10.1103/physreva.50.843 · Cited by 172
Optical Galton board
Bouwmeester, D., Marzoli, I., Karman, G. P., Schleich, W. P., & Woerdman, J. P. (1999) · Physical Review A · doi:10.1103/physreva.61.013410 · Cited by 167
Statistical aspects of dissipation by Landau-Zener transitions
Wilkinson, M. K. (1988) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/21/21/011 · Cited by 169
The Theory of Nonadiabatic Transitions: Recent Development with Exponential Models
Nikitin, E. E. (1970) · Advances in quantum chemistry · doi:10.1016/s0065-3276(08)60338-x · Cited by 169
The role of level anti-crossings in nuclear spin hyperpolarization
Ivanov, K. L., Pravdivtsev, A. N., Yurkovskaya, A. V., et al. (2014) · Progress in Nuclear Magnetic Resonance Spectroscopy · doi:10.1016/j.pnmrs.2014.06.001 · Cited by 168
“Mixing of states caused by an LAC is a well-known problem in physics, which is addressed, for instance, by the Landau–Zener theory [92,93].”
Method
Theory and calculation for the electronic coupling in excitation energy transfer
You, Z., & Hsu, C. (2013) · International Journal of Quantum Chemistry · doi:10.1002/qua.24528 · Cited by 163
Interchange of Charge between Gaseous Molecules in Resonant and Near-Resonant Processes
Gurnee, E. F., & Magee, J. L. (1957) · The Journal of Chemical Physics · doi:10.1063/1.1743499 · Cited by 168
Theory of nonadiabatic transition for general two-state curve crossing problems. II. Landau–Zener case
Zhu, C., & Nakamura, H. (1995) · The Journal of Chemical Physics · doi:10.1063/1.469057 · Cited by 167
Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators
Oka, T., & Aoki, H. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.137601 · Cited by 166
Topology-Induced Anomalous Defect Production by Crossing a Quantum Critical Point
Bermúdez, A., Patanè, D., Luigi Amico, A., & Martin-Delgado, M. A. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.135702 · Cited by 159
Observation of Feshbach Resonances in an Ultracold Gas of Cr52
Werner, J., Griesmaier, A., Hensler, S., Stühler, J., Pfau, T., Simoni, A., & Tiesinga, E. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.183201 · Cited by 162
Excited‐State Electron Transfer
Meyer, T. J. (1983) · Progress in inorganic chemistry · doi:10.1002/9780470166314.ch8 · Cited by 164
Combustion chemistry in the twenty-first century: Developing theory-informed chemical kinetics models
MILLER, J. A., Sivaramakrishnan, R., Tao, Y., Goldsmith, C. F., Burke, M. P., Jasper, A. W., Hansen, N., Labbe, N. J., Glarborg, P., & Zádor, J. (2021) · Progress in Energy and Combustion Science · doi:10.1016/j.pecs.2020.100886 · Cited by 165
Adiabatic-impulse approximation for avoided level crossings: From phase-transition dynamics to Landau-Zener evolutions and back again
Damski, B., & Zurek, W. H. (2006) · Physical Review A · doi:10.1103/physreva.73.063405 · Cited by 162
Mathematical and computational methods for semiclassical Schrödinger equations
Jin, S., Markowich, P. A., & Sparber, C. (2011) · Acta Numerica · doi:10.1017/s0962492911000031 · Cited by 153
“Thus, as long as one is only interested in physical observables, one can simply take S(t, x) = ∫ x a v(t, y) dy (9.14) in the numerical simulations.”
BackgroundInfluential
Engineering novel optical lattices
Windpassinger, P., & Sengstock, K. (2013) · Reports on Progress in Physics · doi:10.1088/0034-4885/76/8/086401 · Cited by 165
“This effect has been fist described by Zener (1932) and is known as Landau–Zener tunneling.”
Method
Analytically Solvable Driven Time-Dependent Two-Level Quantum Systems
Barnes, E., & Sarma, S. D. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.060401 · Cited by 161
Predissociation and photodissociation of IBr
Child, M. S. (1976) · Molecular Physics · doi:10.1080/00268977600102861 · Cited by 160
Perturbation of nuclear spin polarizations in solid state NMR of nitroxide-doped samples by magic-angle spinning without microwaves
Thurber, K. R., & Tycko, R. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4874341 · Cited by 165
Nonadiabatic Landau-Zener tunneling in Fe 8 molecular nanomagnets
Wernsdorfer, W., Sessoli, R., Caneschi, A., et al. (2000) · Europhysics Letters (EPL) · doi:10.1209/epl/i2000-00305-x · Cited by 159
Evolution of molecular dissociation through an electronic curve crossing: Polarized emission spectroscopy of CH3I at 266 nm
Lao, K. Q., Person, M. D., Xayariboun, P., et al. (1990) · The Journal of Chemical Physics · doi:10.1063/1.458116 · Cited by 159
Adiabatic processes in frequency conversion
Suchowski, H., Porat, G., & Arie, A. (2013) · Laser & Photonics Review · doi:10.1002/lpor.201300107 · Cited by 156
Molecular dynamics in electronically excited states using time-dependent density functional theory
Tavernelli, I., Röhrig, U. F., & Röthlisberger, U. (2005) · Molecular Physics · doi:10.1080/00268970512331339378 · Cited by 152
Quenching dynamics of a quantum XY spin- 12 chain in a transverse field
Mukherjee, V., Divakaran, U., Dutta, A., & Sen, D. (2007) · Physical Review B · doi:10.1103/physrevb.76.174303 · Cited by 153
Quantum systems under frequency modulation
Silveri, M., Tuorila, J., Thuneberg, E. V., & Paraoanu, G. S. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa5170 · Cited by 157
“In the following, we give an alternative interpretation to the origin of the increased excited state population in terms of Landau–Zener–Stückelberg (LZS) interference [1, 3, 4].”
Background
Quantitative Conditions Do Not Guarantee the Validity of the Adiabatic Approximation
Tong, D. M., Singh, K., Kwek, L. C., & Oh, C. H. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.110407 · Cited by 153
An Efficient, Augmented Surface Hopping Algorithm That Includes Decoherence for Use in Large-Scale Simulations
Jain, A., Alguire, E. C., & Subotnik, J. E. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00673 · Cited by 152
S-matrix for generalized Landau-Zener problem
Brundobler, S., & Elser, V. (1993) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/26/5/037 · Cited by 150
Large Momentum Beam Splitter Using Bloch Oscillations
Cladé, P., Guellati-Khélifa, S., Nez, F., & Biraben, F. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.240402 · Cited by 163
What are the basic mechanisms of electronic transitions in molecular dynamic processes?
Nakamura, H. (1991) · International Reviews in Physical Chemistry · doi:10.1080/01442359109353256 · Cited by 147
Charge exchange between H(1s) and fully stripped heavy ions at low-keV impact energies
Salop, A., & Olson, R. E. (1976) · Physical Review A · doi:10.1103/physreva.13.1312 · Cited by 147
Slow non-Hermitian cycling: exact solutions and the Stokes phenomenon
Berry, M., & Uzdin, R. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/43/435303 · Cited by 146
Spin-parity dependent tunneling of magnetization in single-molecule magnets
Wernsdorfer, W., Bhaduri, S., Boskovic, C., et al. (2002) · Physical review. B, Condensed matter · doi:10.1103/physrevb.65.180403 · Cited by 146
Predissociation and the Crossing of Molecular Potential Energy Curves
Rice, O. K. (1933) · The Journal of Chemical Physics · doi:10.1063/1.1749305 · Cited by 145
Nonequilibrium Dynamic Critical Scaling of the Quantum Ising Chain
Kolodrubetz, M., Clark, B. K., & Huse, D. A. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.015701 · Cited by 143
Charge transfer
Bates, D. R., & McCarroll, R. (1962) · Advances In Physics · doi:10.1080/00018736200101262 · Cited by 144
Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime
Kowalewski, M., Fingerhut, B. P., Dorfman, K. E., Bennett, K., & Mukamel, S. (2017) · Chemical Reviews · doi:10.1021/acs.chemrev.7b00081 · Cited by 145
Direct mapping of curve-crossing dynamics in IBr by attosecond transient absorption spectroscopy
Kobayashi, Y., Chang, K. F., Zeng, T., Neumark, D. M., & Leone, S. R. (2019) · Science · doi:10.1126/science.aax0076 · Cited by 142
Non-Born-Oppenheimer Liouville-von Neumann Dynamics. Evolution of a Subsystem Controlled by Linear and Population-Driven Decay of Mixing with Decoherent and Coherent Switching
Zhu, C., Jasper, A. W., & Truhlar, D. G. (2005) · Journal of Chemical Theory and Computation · doi:10.1021/ct050021p · Cited by 141
Schwinger mechanism revisited
Cohen, T. D., & McGady, D. A. (2008) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.78.036008 · Cited by 142
Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior
Saito, K., Wubs, M., Kohler, S., Kayanuma, Y., & Peter Hänggi, A. (2007) · Physical Review B · doi:10.1103/physrevb.75.214308 · Cited by 145
Collisional ionization and elastic scattering in alkali–halogen atom collisions
Faist, M. B., & Levine, R. D. (1976) · The Journal of Chemical Physics · doi:10.1063/1.432555 · Cited by 142
On the multidimensional surface intersection problem and classical trajectory ’’surface hopping’’
Stine, J. R., & Muckerman, J. T. (1976) · The Journal of Chemical Physics · doi:10.1063/1.432892 · Cited by 142
High efficiency transfer of quantum information and multiparticle entanglement generation in translation-invariant quantum chains
Plenio, M. B., & Semião, F. L. (2005) · New Journal of Physics · doi:10.1088/1367-2630/7/1/073 · Cited by 140
Many-body Landau–Zener dynamics in coupled one-dimensional Bose liquids
Chen, Y.-A., Huber, S. D., Trotzky, S., Bloch, I., & Altman, E. (2010) · Nature Physics · doi:10.1038/nphys1801 · Cited by 140
“The basic prototype of such phenomena is the Landau–Zener (LZ) problem, which describes a sweep through an anti-crossing of two level”
Background
From reversible quantum microdynamics to irreversible quantum transport
Rau, J., & Müller, B. (1996) · Physics Reports · doi:10.1016/0370-1573(95)00077-1 · Cited by 141
A critique of Zwaan-Stueckelberg phase integral techniques
Crothers, D. S. F. (1971) · Advances In Physics · doi:10.1080/00018737100101281 · Cited by 139
Dynamics after a sweep through a quantum critical point
Pollmann, F., Mukerjee, S., Green, A. G., & Moore, J. E. (2010) · Physical Review E · doi:10.1103/physreve.81.020101 · Cited by 139
Valence bond theory for chemical dynamics
Truhlar, D. G. (2006) · Journal of Computational Chemistry · doi:10.1002/jcc.20529 · Cited by 139
Magnetic Quantum Tunneling in the Single-Molecule Magnet Mn12-Acetate
del Barco, E., Kent, A. D., Hill, S., et al. (2005) · Journal of Low Temperature Physics · doi:10.1007/s10909-005-6016-3 · Cited by 137
Enhancement of magnon-magnon entanglement inside a cavity
Yuan, H. Y., Zheng, S., Ficek, Z., He, Q., & Yung, M. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.101.014419 · Cited by 137
Theory of coupled ion-electron transfer kinetics
Fraggedakis, D., McEldrew, M., Smith, R. B., Krishnan, Y., Zhang, Y. A., Bai, P., Chueh, W. C., Shao‐Horn, Y., & Bazant, M. Z. (2020) · Electrochimica Acta · doi:10.1016/j.electacta.2020.137432 · Cited by 138
“The tunneling of electrons is modeled using the Landau-Zener theory [82, 83].”
Method
Control of Electron Transfer Kinetics: Models for Medium Reorganization and Donor–Acceptor Coupling
Newton, M. D. (1999) · Advances in chemical physics · doi:10.1002/9780470141656.ch7 · Cited by 137
Electric-field-induced metal maintained by current of the Mott insulator Ca2RuO4
Nakamura, F., Sakaki, M., Yamanaka, Y., Tamaru, S., Suzuki, T., & Maeno, Y. (2013) · Scientific Reports · doi:10.1038/srep02536 · Cited by 136
Theoretical aspects of Magic Angle Spinning - Dynamic Nuclear Polarization
Mentink‐Vigier, F., Akbey, Ü., Oschkinat, H., Vega, S., & Feintuch, A. (2015) · Journal of Magnetic Resonance · doi:10.1016/j.jmr.2015.07.001 · Cited by 140
Collision processes involving heavy many-electron ions interacting with neutral atoms
TOLSTIKHINA, I. Y., & Shevelko, V. P. (2013) · Physics-Uspekhi · doi:10.3367/ufne.0183.201303a.0225 · Cited by 135
Experimental probing of conical intersection dynamics in the photodissociation of thioanisole
Lim, J. S., & Kim, S. K. (2010) · Nature Chemistry · doi:10.1038/nchem.702 · Cited by 134
“Therefore, a higher non-adiabatic transition probability at CI-2 that leads to C 6 H 5 S•( ) is expected for fragments with a higher relative translational energy, as predicted by the Landau–Zener formul”
Method
Transient excitons at metal surfaces
Cui, X., Wang, C., Argondizzo, A., et al. (2014) · Nature Physics · doi:10.1038/nphys2981 · Cited by 135
Slow quenches in a quantum Ising chain: Dynamical phase transitions and topology
Sharma, S., Divakaran, U., Polkovnikov, A., et al. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.144306 · Cited by 135
Gauging a Quantum Heat Bath with Dissipative Landau-Zener Transitions
Wubs, M., Saito, K., Kohler, S., Peter Hänggi, A., & Kayanuma, Y. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.200404 · Cited by 137
Photodissociation processes in the CH molecule
van Dishoeck, E. F. (1987) · The Journal of Chemical Physics · doi:10.1063/1.452610 · Cited by 135
The production of K shell vacancies in symmetric ion-atom collisions
Briggs, J. S., & Macek, J. H. (1972) · Journal of Physics B Atomic and Molecular Physics · doi:10.1088/0022-3700/5/3/025 · Cited by 135
The spin-forbidden reaction CH(2Π)+N2→HCN+N(4S) revisited. II. Nonadiabatic transition state theory and application
Cui, Q., Morokuma, K., Bowman, J. M., & Klippenstein, S. J. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478949 · Cited by 132
Intense laser-field ionization of H2 enhanced by two-electron dynamics
Harumiya, K., Kono, H., Fujimura, Y., Kawata, I., & Bandrauk, A. D. (2002) · Physical Review A · doi:10.1103/physreva.66.043403 · Cited by 132
Resonant neutrino oscillations in matter
Mikheyev, S., & Smirnov, A. Y. (1989) · Progress in Particle and Nuclear Physics · doi:10.1016/0146-6410(89)90008-2 · Cited by 134
Time-dependent tunneling of Bose-Einstein condensates
Zobay, O., & Garraway, B. M. (2000) · Physical Review A · doi:10.1103/physreva.61.033603 · Cited by 133
Bloch-Zener Oscillations across a Merging Transition of Dirac Points
Lim, L.-K., Fuchs, J.-N., & Montambaux, G. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.175303 · Cited by 134
Gravitational collider physics
Baumann, D., Chia, H. S., Porto, R. A., & Stout, J. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.083019 · Cited by 163
Solar-Neutrino Problem and Three-Neutrino Oscillations
Kuo, T. K., & Pantaleone, J. T. (1986) · Physical Review Letters · doi:10.1103/physrevlett.57.1805 · Cited by 132
Adiabatic and diabatic responses of H2+ to an intense femtosecond laser pulse: Dynamics of the electronic and nuclear wave packet
Kawata, I., Kono, H., & Fujimura, Y. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478002 · Cited by 131
Photofragmentation of CH3Br in the A band
van Veen, G. N. A., Baller, T., & Vries, A. E. D. (1985) · Chemical Physics · doi:10.1016/0301-0104(85)80005-7 · Cited by 131
Time-Averaged Adiabatic Potentials: Versatile Matter-Wave Guides and Atom Traps
Lesanovsky, I., & von Klitzing, W. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.083001 · Cited by 130
Inelastic atom-atom scattering within an intense laser beam
Kroll, N. M., & Watson, K. (1976) · Physical Review A · doi:10.1103/physreva.13.1018 · Cited by 130
Evaluation of the Time-Derivative Coupling for Accurate Electronic State Transition Probabilities from Numerical Simulations
Meek, G. A., & Levine, B. G. (2014) · The Journal of Physical Chemistry Letters · doi:10.1021/jz5009449 · Cited by 128
Time-Resolved Measurement of Landau-Zener Tunneling in Periodic Potentials
Zenesini, A., Lignier, H., Tayebirad, G., et al. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.090403 · Cited by 128
Sign- and Magnitude-Tunable Coupler for Superconducting Flux Qubits
Harris, R., Berkley, A. J., Johnson, M. W., Bunyk, P., Govorkov, S. A., Thom, M. C., Uchaikin, S. V., Wilson, A. B., Chung, J., Holtham, E., et al. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.177001 · Cited by 127
Single-Molecule Nanomagnets
Friedman, J. R., & Sarachik, M. P. (2010) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-070909-104053 · Cited by 133
The quantum adiabatic algorithm applied to random optimization problems: The quantum spin glass perspective
Bapst, V., Foini, L., Krząkała, F., Semerjian, G., & Zamponi, F. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.10.002 · Cited by 135
“The advantage of this simplified formulation is that it is exactly solvable in the limit of an evolution going from s = −∞ to s =∞, the Landau-Zener formula [97, 98] giving the probability P of a diabatic transition to an excited state as P = e−2T πγ 2/b, which has for consequence the necessary condition for an adiaba…”
Background
Electronic and Optical Properties of Graphene Quantum Dots: The Role of Many-Body Effects
Li, Y., Shu, H., Wang, S., & Wang, J. (2015) · The Journal of Physical Chemistry C · doi:10.1021/jp506969r · Cited by 126
Extracting the Chern Number from the Dynamics of a Fermi Gas: Implementing a Quantum Hall Bar for Cold Atoms
Dauphin, A., & Goldman, N. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.135302 · Cited by 124
Nonadiabatic Dynamics of Two Strongly Coupled Nanomechanical Resonator Modes
Faust, T., Rieger, J., Seitner, M. J., Krenn, P., Kotthaus, J. P., & Weig, E. M. (2012) · Physical Review Letters · doi:10.1103/physrevlett.109.037205 · Cited by 132
Quasi-diabatic states and dynamical couplings from ab initio CI calculations: a new proposal
Cimiraglia, R., Malrieu, J., Persico, M., et al. (1985) · Journal of Physics B Atomic and Molecular Physics · doi:10.1088/0022-3700/18/15/014 · Cited by 125
State selective photodissociation dynamics of A state ammonia. I
Biesner, J., Schnieder, L., Schmeer, J., et al. (1988) · The Journal of Chemical Physics · doi:10.1063/1.453910 · Cited by 125
Approaches to nuclear friction
Hasse, R. W. (1978) · Reports on Progress in Physics · doi:10.1088/0034-4885/41/7/002 · Cited by 124
Topological phases, Majorana modes and quench dynamics in a spin ladder system
DeGottardi, W., Sen, D., & Vishveshwara, S. (2011) · New Journal of Physics · doi:10.1088/1367-2630/13/6/065028 · Cited by 126
Diabatic and adiabatic representations for atomic collision processes
Delos, J. B., & Thorson, W. R. (1979) · The Journal of Chemical Physics · doi:10.1063/1.437650 · Cited by 122

Authors: Zener, C.
Affiliations: National Research Fellow of U. S. A.
Corresponding author: Zener, Clarence
Venue: Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character
Publisher: The Royal Society
Published: 1932-09-01
Volume: 137
Issue: 833
Pages: 696-702
ISSN: 0950-1207 (ISSN-L)
2053-9150
DOI: 10.1098/rspa.1932.0165
OpenAlex: W1981659415
Cited by: 4,572
References: 0
Citations by year: 2026: 92 · 2025: 129 · 2024: 121 · 2023: 141 · 2022: 147 · 2021: 137 · 2020: 138 · 2019: 158 · 2018: 173 · 2017: 156 · 2016: 156 · 2015: 145 · 2014: 160 · 2013: 164 · 2012: 116
FWCI: 1.52
Type: journal article
Language: en
Open access: diamond
doi.org
Licence: royalsociety.org/journals/ethics-policies/data-sharing-mining/ (tdm)
Locations: Proceedings of the Royal Society of London Series A Containing Papers of a Mathematical and Physical Character (publishedVersion)
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Molecular Physics
Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Keywords: energy level crossing, molecular electronic states, diatomic molecules, adiabatic approximation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Non-adiabatic crossing of energy levels

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Claims other papers make about this one

Citations

Cited by

Related

Metadata

Record

About these checks