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arXiv:2512.07484 · Physical Review Research

Anomalous Wave-Packet Dynamics in One-Dimensional Non-Hermitian Lattices

Yanyan He, Tomoki Ozawa

physics.opticscond-mat.dis-nnquant-phSubmitted Dec 8, 2025• Announced Dec 9, 2025• 3 citations• Revised Dec 15, 2025 (v2)
v1 · Dec 8, 2025v2 · Dec 15, 2025v3 · May 26, 2026
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Abstract

Non-Hermitian (NH) systems have attracted great attention due to their exotic phenomena beyond Hermitian domains. Here we study the wave-packet dynamics in general one-dimensional NH lattices and uncover several unexpected phenomena. The group velocity of a wave packet during the time evolution in such NH lattices is not only governed by the real part of the band structure but also by its imaginary part. The momentum also evolves due to the imaginary part of the band structure, which can lead to a self-induced Bloch oscillation in the absence of external fields. Furthermore, we discover the wave-packet dynamics can exhibit disorder-free NH jumps even when the energy spectra are entirely real. Finally, we show that the NH jumps can lead to both positive and negative temporal Goos--Hänchen shifts at the edge.

Journal reference
Physical Review Research 8, L032044 (2026)
DOI
10.1103/t7qp-wr19

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Non-Hermitian (NH) systems have attracted great attention due to their exotic phenomena beyond Hermitian domains. Here we study the wave-packet dynamics in general one-dimensional NH lattices and uncover several unexpected phenomena. The group velocity of a wave packet during the time evolution in such NH lattices is not only governed by the real part of the band structure but also by its imaginary part. The momentum also evolves due to the imaginary part of the band structure, which can lead to a self-induced Bloch oscillation in the absence of external fields. Furthermore, we discover the wave-packet dynamics can exhibit disorder-free NH jumps even when the energy spectra are entirely real. Finally, we show that the NH jumps can lead to both positive and negative temporal Goos--Hänchen shifts at the edge.
Bloch oscillations (BOs) represent a paradigmatic manifestation of force-driven band dynamics in lattices, conventionally characterized by continuous quasimomentum evolution and smooth periodic trajectories. Here we show that non-Hermiticity qualitatively changes this paradigm, introducing nonsmooth BOs characterized by cusp-like real-space trajectories and abrupt momentum jumps. Reversing the force switches the dynamics between smooth and nonsmooth BOs, enabling strongly nonreciprocal dynamics. We derive a universal relation for the critical force that governs the nonsmooth-to-smooth dynamical transition in general one-dimensional lattices, which is induced by a pitchfork bifurcation in momentum space. Our work establishes a unified framework for non-Hermitian BOs and uncovers a fundamental bifurcation mechanism that can generate nonsmooth wave transport in entirely linear systems.
Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and PT -symmetric examples are studied, a Hatano–Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.
This paper investigates wave-packet dynamics in non-Hermitian lattice systems and reveals a surprising phenomenon: The simultaneous propagation of two distinct wavefronts, one traveling at the non-Hermitian velocity and the other at the Hermitian velocity. We show that this dual-front behavior arises naturally in systems governed by a pseudo-Hermitian Hamiltonian. Using the paradigmatic Hatano-Nelson model as our primary example, we demonstrate that this coexistence is essential for understanding a wide array of unconventional dynamical effects, including abrupt ``non-Hermitian reflections'', sudden shifts of Gaussian wave-packets, and disorder-induced emergent packets seeded by the small initial tails. We present analytic predictions that closely match numerical simulations. These results may offer new insight into the topology of non-Hermitian systems and point toward measurable experimental consequences.
We consider non-Hermitian dynamics of a quantum particle hopping on a one-dimensional tight-binding lattice made of NNN sites with asymmetric hopping rates induced by a time-periodic oscillating imaginary gauge field. A deeply different behavior is found depending on the lattice topology. While in a linear chain (open boundary conditions) an oscillating field can lead to a complex quasienergy spectrum via a multiple parametric resonance; in a ring topology (Born--von Karman periodic boundary conditions) an entirely real quasienergy spectrum can be found and the dynamics is pseudo-Hermitian. In the large-NNN limit, parametric instability and pseudo-Hermitian dynamics in the two different lattice topologies are physically explained on the basis of a simple picture of wave-packet propagation.
Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.
We investigate the band structure and topological phases of one- and two-dimensional bipartite atomic lattices mediated by long-range dissipative radiative coupling. By deriving an effective non-Hermitian Hamiltonian for the single-excitation sector, we demonstrate that the low-energy dynamics of the system are governed by a Dirac equation with a complex Fermi velocity. We analyze the associated topological invariants for both the SSH and honeycomb models, utilizing synthetic gauge fields to break time-reversal symmetry in the latter. Finally, we explicitly verify the non-Hermitian bulk-edge correspondence by deriving analytical solutions for edge states localized at domain boundaries.